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Control Problem (control + problem)
Kinds of Control Problem Selected AbstractsOPTIMAL DISCOUNTING IN CONTROL PROBLEMS THAT SPAN MULTIPLE GENERATIONSNATURAL RESOURCE MODELING, Issue 3 2005FRANK CALIENDO ABSTRACT. The principal contribution of this paper is the linking together of separate control problems across multiple generations using the bequest motive, intergenerational altruism, rational expectations, and solution boundary conditions. We demonstrate that discounting at the market rate of interest is an endogenous characteristic of a general equilibrium, optimal control problem that spans multiple generations. Within the confines of our model, we prove that it is optimal to discount at the market rate of interest the social benefits to distant generations from immediate clean up at toxic waste sites if the current generation that bears the cleanup cost is perfectly altruistic towards future generations. Also, we show that this result holds for alternative assumptions regarding pure time preference. Moreover, the result holds regardless of whether selfish interim generations attempt to undo the provisions made for distant generations. In our distortion-free deterministic model, the evidence for intergenerational discounting at the market rate of interest is compelling. [source] Robust H, Control Problem For General Nonlinear Systems With UncertaintyASIAN JOURNAL OF CONTROL, Issue 2 2003Jenq-Lang Wu ABSTRACT In this paper, both state and output feedback robust H, control problems for general nonlinear systems with norm-bound uncertainty are considered. Sufficient conditions for the existence of robust output feedback H, controller are provided. State space formulas for robust H, output controller are provided. [source] Generalizations of Optimal Control Problems by ComparisonPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003H. Irrgang Dr. Generalizations of optimal control problems can be used for deciding the existence of solutions as well as for constructions of approximate solutions. In such cases one has to ask for gaps between the original problem and its generalizations. An overview will be given on several generalizations of a special kind of optimal control problems and the connections between them will be pointed out. These connections allow to answer the question about gaps for special cases. [source] Control problems with surfaces triggering jumps in the state variablesOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 2 2010Atle Seierstad Abstract By means of some simple examples from economics, we elucidate certain solution tools for the solution of optimal control problems where the system under study undergoes major changes when certain boundaries are crossed. The ,major changes' may be that the state jumps when crossing a boundary, or that the right-hand side of the differential equation changes. Some theoretical results are also presented. In Appendix more or less sketchy proofs of these results are given. Copyright © 2009 John Wiley & Sons, Ltd. [source] Robust active vibration suppression control with constraint on the control signal: application to flexible structuresEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 11 2003A. Forrai Abstract A unified mathematical framework, sustained by experimental results, is presented for robust controller design taking into account the constraint on the control signal. The design procedure is exemplified for an active vibration suppression control problem with applications to flexible structures. The considered experimental set-up is a three-storey flexible structure with an active mass driver placed on the last storey. First, the considered flexible structure is identified and the model's parametric uncertainties are deduced. Next, control constraints are presented for the robust control design problem, taking into account the restriction imposed on the control signal. Finally, the effectiveness of the control system is tested through experiments, when the input disturbance is assumed to be a sinusoidal one as well as a historical earthquake record (1940 El Centro record). Copyright © 2003 John Wiley & Sons, Ltd. [source] Baghouse system design based on economic optimizationENVIRONMENTAL PROGRESS & SUSTAINABLE ENERGY, Issue 4 2000Antonio C. Caputo In this paper a method is described for using economic optimization in the design of baghouse systems. That is, for a given emission control problem, the total filtration surface area, the overall pressure drop, fabric material effects, and the cleaning cycle frequency, may all be evaluated simultaneously. In fact, as baghouse design parameters affect capital and operating expenses in interrelated and counteracting manners, a minimum total cost may be searched defining the best arrangement of dust collection devices. With this in mind, detailed cost functions have been developed with the aim of providing an overall economic model. As a result, a discounted total annual cost has been obtained that may be minimized by allowing for optimal baghouse characterization. Finally, in order to highlight the capabilities of the proposed methodology, some optimized solutions are also presented, which consider the economic impact of both bag materials and dust properties. [source] Optimal Control of Rigid-Link Manipulators by Indirect MethodsGAMM - MITTEILUNGEN, Issue 1 2008Rainer Callies Abstract The present paper is a survey and research paper on the treatment of optimal control problems of rigid-link manipulators by indirect methods. Maximum Principle based approaches provide an excellent tool to calculate optimal reference trajectories for multi-link manipulators with high accuracy. Their major drawback was the need to explicitly formulate the complicated system of adjoint differential equations and to apply the full apparatus of optimal control theory. This is necessary in order to convert the optimal control problem into a piecewise defined, nonlinear multi-point boundary value problem. An accurate and efficient access to first- and higher-order derivatives is crucial. The approach described in this paper allows it to generate all the derivative information recursively and simultaneously with the recursive formulation of the equations of motion. Nonlinear state and control constraints are treated without any simplifications by transforming them into sequences of systems of linear equations. By these means, the modeling of the complete optimal control problem and the accompanying boundary value problem is automated to a great extent. The fast numerical solution is by the advanced multiple shooting method JANUS. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Knowledge transfer costs and dependence as determinants of financial reportingACCOUNTING & FINANCE, Issue 3 2003David Hay Abstract This paper examines the circumstances in which financial reporting exists. Jensen and Meckling (1995) observe that where there are high knowledge transfer costs, then decentralisation is necessary; and that where decentralisation occurs there is a control problem, which can be addressed by providing a control system. I predict that where there are high knowledge transfer costs there will be a control system; if the control system uses financial reports, these will occur for activities with high knowledge transfer costs. The ability to decentralise is reduced where dependence makes it potentially costly to allow a subordinate to make decisions about the activity. The paper predicts that high dependence will be negatively associated with the existence of financial reports. The results confirm the predictions that financial reports are positively associated with knowledge transfer costs and negatively associated with dependence. [source] Solving inverse electromagnetic problems using FDTD and gradient-based minimizationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2006Erik Abenius Abstract We address time-domain inverse electromagnetic scattering for determining unknown characteristics of an object from observations of the scattered field. Applications include non-destructive characterization of media and optimization of material properties, for example, the design of radar absorbing materials. Another application is model reduction where a detailed model of a complex geometry is reduced to a simplified model. The inverse problem is formulated as an optimal control problem where the cost function to be minimized is the difference between the estimated and observed fields, and the control parameters are the unknown object characteristics. The problem is solved in a deterministic gradient-based optimization algorithm using a parallel 2D FDTD scheme. Highly accurate analytical gradients are computed from the adjoint formulation. The inverse method is applied to the characterization of layered dispersive media and the determination of parameters in subcell models for thin sheets and narrow slots. Copyright © 2006 John Wiley & Sons, Ltd. [source] Optimal flow control for Navier,Stokes equations: drag minimizationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2007L. Dedč Abstract Optimal control and shape optimization techniques have an increasing role in Fluid Dynamics problems governed by partial differential equations (PDEs). In this paper, we consider the problem of drag minimization for a body in relative motion in a fluid by controlling the velocity through the body boundary. With this aim, we handle with an optimal control approach applied to the steady incompressible Navier,Stokes equations. We use the Lagrangian functional approach and we consider the Lagrangian multiplier method for the treatment of the Dirichlet boundary conditions, which include the control function itself. Moreover, we express the drag coefficient, which is the functional to be minimized, through the variational form of the Navier,Stokes equations. In this way, we can derive, in a straightforward manner, the adjoint and sensitivity equations associated with the optimal control problem, even in the presence of Dirichlet control functions. The problem is solved numerically by an iterative optimization procedure applied to state and adjoint PDEs which we approximate by the finite element method. Copyright © 2007 John Wiley & Sons, Ltd. [source] Dynamical systems-based optimal control of incompressible fluidsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2004Michael Hintermüller Abstract For optimal control problems related to fluid flow the choice of an adequate cost functional for suppression of vortices is of significant importance. In this research we propose a cost functional based on a local dynamical systems characterization of vortices. The resulting functional is a non-convex function of the velocity gradient tensor. The resulting optimality system describing first order necessary optimality conditions is derived, a possible strategy for numerical realization of the optimal control problem is provided and a numerical feasibility study is conducted. Copyright © 2004 John Wiley & Sons, Ltd. [source] Numerical approximation of optimal control of unsteady flows using SQP and time decompositionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2004S. S. RavindranArticle first published online: 1 APR 200 Abstract In this paper, we present numerical approximations of optimal control of unsteady flow problems using sequential quadratic programming method (SQP) and time domain decomposition. The SQP method is considered superior due to its fast convergence and its ability to take advantage of existing numerical techniques for fluid flow problems. It iteratively solves a sequence of linear quadratic optimal control problems converging to the solution of the non-linear optimal control problem. The solution to the linear quadratic problem is characterized by the Karush,Kuhn,Tucker (KKT) optimality system which in the present context is a formidable system to solve. As a remedy various time domain decompositions, inexact SQP implementations and block iterative methods to solve the KKT systems are examined. Numerical results are presented showing the efficiency and feasibility of the algorithms. Copyright © 2004 John Wiley & Sons, Ltd. [source] Suppression of vortex shedding for flow around a circular cylinder using optimal controlINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2002C. Homescu Abstract Adjoint formulation is employed for the optimal control of flow around a rotating cylinder, governed by the unsteady Navier,Stokes equations. The main objective consists of suppressing Karman vortex shedding in the wake of the cylinder by controlling the angular velocity of the rotating body, which can be constant in time or time-dependent. Since the numerical control problem is ill-posed, regularization is employed. An empirical logarithmic law relating the regularization coefficient to the Reynolds number was derived for 60,Re,140. Optimal values of the angular velocity of the cylinder are obtained for Reynolds numbers ranging from Re=60 to Re=1000. The results obtained by the computational optimal control method agree with previously obtained experimental and numerical observations. A significant reduction of the amplitude of the variation of the drag coefficient is obtained for the optimized values of the rotation rate. Copyright © 2002 John Wiley & Sons, Ltd. [source] Adaptive controller design and disturbance attenuation for SISO linear systems with zero relative degree under noisy output measurementsINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 4 2010Sheng Zeng Abstract In this paper, we present robust adaptive controller design for SISO linear systems with zero relative degree under noisy output measurements. We formulate the robust adaptive control problem as a nonlinear H, -optimal control problem under imperfect state measurements, and then solve it using game theory. By using the a priori knowledge of the parameter vector, we apply a soft projection algorithm, which guarantees the robustness property of the closed-loop system without any persistency of excitation assumption of the reference signal. Owing to our formulation in state space, we allow the true system to be uncontrollable, as long as the uncontrollable part is stable in the sense of Lyapunov, and the uncontrollable modes on the j,-axis are uncontrollable from the exogenous disturbance input. This assumption allows the adaptive controller to asymptotically cancel out, at the output, the effect of exogenous sinusoidal disturbance inputs with unknown magnitude, phase, and frequency. These strong robustness properties are illustrated by a numerical example. Copyright © 2009 John Wiley & Sons, Ltd. [source] Design of adaptive variable structure controllers for T,S fuzzy time-delay systemsINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 2 2010Tai-Zu Wu Abstract In this paper, the adaptive variable structure control problem is presented for Takagi,Sugeno (T,S) fuzzy time-delay systems with uncertainties and external disturbances. The fuzzy sliding surfaces for the T,S fuzzy time-delay system are proposed by using a Lyapunov function, and we design the adaptive variable structure controllers such that the global T,S fuzzy time-delay system confined on the fuzzy sliding surfaces is asymptotically stable. One example is given to illustrate the effectiveness of our proposed methods. Copyright © 2009 John Wiley & Sons, Ltd. [source] Finite-model adaptive control using an LS-like algorithm,INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 5 2007Hongbin Ma Abstract Adaptive control problem of a class of discrete-time nonlinear uncertain systems, of which the internal uncertainty can be characterized by a finite set of functions, is formulated and studied by using an least squares (LS)-like algorithm to design the feedback control law. For the finite-model adaptive control problem, this algorithm is proposed as an extension of counterpart of traditional LS algorithm. Stability in sense of pth mean for the closed-loop system is proved under a so-called linear growth assumption, which is shown to be necessary in general by a counter-example constructed in this paper. The main results have been also applied to parametric cases, which demonstrate how to bridge the non-parametric case and parametric case. Copyright © 2006 John Wiley & Sons, Ltd. [source] Optimality for the linear quadratic non-Gaussian problem via the asymmetric Kalman filterINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 1 2004Rosario Romera Abstract In the linear non-Gaussian case, the classical solution of the linear quadratic Gaussian (LQG) control problem is known to provide the best solution in the class of linear transformations of the plant output if optimality refers to classical least-squares minimization criteria. In this paper, the adaptive linear quadratic control problem is solved with optimality based on asymmetric least-squares approach, which includes least-squares criteria as a special case. Our main result gives explicit solutions for this optimal quadratic control problem for partially observable dynamic linear systems with asymmetric observation errors. The main difficulty is to find the optimal state estimate. For this purpose, an asymmetric version of the Kalman filter based on asymmetric least-squares estimation is used. We illustrate the applicability of our approach with numerical results. Copyright © 2004 John Wiley & Sons, Ltd. [source] Adaptive control of continuous time stochastic systemsINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 5 2002T.E. Duncan Abstract Some problems and solutions of adaptive control problems for continuous time stochastic systems are described. A solution is given to the adaptive linear quadratic Gaussian control problem under the natural assumptions of controllability and observability. The effects of sampling and numerical differentiation on a least-squares estimation algorithm are described. Adaptive control problems for non-linear stochastic systems and linear stochastic distributed parameter systems are briefly described. Copyright © 2002 John Wiley & Sons, Ltd. [source] Virtual reference feedback tuning for two degree of freedom controllersINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 5 2002A. Lecchini The virtual reference feedback tuning (VRFT) is a data-based method for the design of feedback controllers. In the original formulation, the VRFT method gives a solution to the degree of freedom model-reference control problem in which the objective is to shape the input,output transfer function of the control system. In this paper, the extension of the method to the design of 2 d.o.f. controllers is presented and discussed. Copyright © 2002 John Wiley & Sons, Ltd. [source] Multiple model adaptive control with safe switchingINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 5 2001Brian D. O. Anderson Abstract The purpose of this paper is to marry the two concepts of multiple model adaptive control and safe adaptive control. In its simplest form, multiple model adaptive control involves a supervisor switching among one of a finite number of controllers as more is learnt about the plant, until one of the controllers is finally selected and remains unchanged. Safe adaptive control is concerned with ensuring that when the controller is changed in an adaptive control algorithm, the frozen plant,controller combination is never (closed-loop) unstable. This is a non-trivial task since by definition of an adaptive control problem, the plant is not fully known. The proposed solution method involves a frequency-dependent performance measure and employs the Vinnicombe metric. The resulting safe switching guarantees depend on the extent to which a closed-loop transfer function can be accurately identified. Copyright © 2001 John Wiley & Sons, Ltd. [source] Model reference adaptive control using a low-order controllerINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 3 2001Daniel E. Miller Abstract In the model reference adaptive control problem, the goal is to force the error between the plant output and the reference model output asymptotically to zero. The classical assumptions on a single-input,single-output (SISO) plant is that it is minimum phase, and that the plant relative degree, the sign of the high-frequency gain, and an upper bound on the plant order are known. Here we consider a modified problem in which the objective is weakened slightly to that of requiring that the asymptotic value of the error be less than a (arbitrarily small) pre-specified constant. Using recent results on the design of generalized holds for model reference tracking, here we present a new switching adaptive controller of dimension two which achieves this new objective for every minimum phase SISO system; no structural information is required. Copyright © 2001 John Wiley & Sons, Ltd. [source] Non-inferior Nash strategies for routing control in parallel-link communication networksINTERNATIONAL JOURNAL OF COMMUNICATION SYSTEMS, Issue 4 2005Yong Liu Abstract We consider a routing control problem of two-node parallel-link communication network shared by competitive teams of users. Each team has various types of entities (traffics or jobs) to be routed on the network. The users in each team cooperate for the benefit of their team so as to achieve optimal routing over network links. The teams, on the other hand, compete among themselves for the network resources and each has an objective function that relates to the overall performance of the network. For each team, there is a centralized decision-maker, called the team leader or manager, who coordinates the routing strategies among all entities in his team. A game theoretic approach to deal with both cooperation within each team and competition among the teams, called the Non-inferior Nash strategy, is introduced. Considering the roles of a group manager in this context, the concept of a Non-inferior Nash strategy with a team leader is introduced. This multi-team solution provides a new framework for analysing hierarchically controlled systems so as to address complicated coordination problems among the various users. This strategy is applied to derive the optimal routing policies for all users in the network. It is shown that Non-inferior Nash strategies with a team leader is effective in improving the overall network performance. Various types of other strategies such as team optimization and Nash strategies are also discussed for the purpose of comparison. Copyright © 2005 John Wiley & Sons, Ltd. [source] Design of the fuzzy multiobjective controller based on the eligibility methodINTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 5 2003Hwan-Chun Myung A multiobjective control problem has been handled in many different ways such as fuzzy, neural network and reinforcement learning, etc. Among them, a reinforcement learning method solves a multiobjective control problem without any prior knowledge. In this article, a new reinforcement learning method for a multiobjective control problem is proposed in consideration of its convergence. The proposed method, in which objective eligibility is considered for handling multirewards, reformulates a multiobjective control problem in a form of a reinforcement learning problem under non-Markov environment. Using a similar relation to eligibility, the proposed method dealt with the previous research results of eligibility and was implemented with the concept of a decoupled fuzzy sliding mode control (DFSMC). © 2003 Wiley Periodicals, Inc. [source] Linear quadratic regulation for systems with time-varying delayINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 3 2010Huanshui Zhang Abstract In this paper we study the linear quadratic regulation (LQR) problem for discrete-time systems with time-varying delay in the control input channel. We assume that the time-varying delay is of a known upper bound, then the LQR problem is transformed into the optimal control problem for systems with multiple input channels, each of which has single constant delay. The optimal controller is derived by establishing a duality between the LQR and a smoothing estimation for an associated system with a multiple delayed measurement. Copyright © 2009 John Wiley & Sons, Ltd. [source] Inf,sup control of discontinuous piecewise affine systemsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 13 2009J. Spjřtvold Abstract This paper considers the worst-case optimal control of discontinuous piecewise affine (PWA) systems, which are subjected to constraints and disturbances. We seek to pre-compute, via dynamic programming, an explicit control law for these systems when a PWA cost function is utilized. One difficulty with this problem class is that, even for initial states for which the value function of the optimal control problem is finite, there might not exist a control law that attains the infimum. Hence, we propose a method that is guaranteed to obtain a sub-optimal solution, and where the degree of sub-optimality can be specified a priori. This is achieved by approximating the underlying sub-problems with a parametric piecewise linear program. Copyright © 2008 John Wiley & Sons, Ltd. [source] On linear-parameter-varying (LPV) slip-controller design for two-wheeled vehiclesINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 12 2009Matteo Corno Abstract This paper describes the application of linear-parameter-varying (LPV) control design techniques to the problem of slip control for two-wheeled vehicles. A nonlinear multi-body motorcycle simulator is employed to derive a control-oriented dynamic model. It is shown that, in order to devise a robust controller with good performance, it is necessary to take into account the dependence of the model on the velocity and on the wheel slip. This dependence is modeled via an LPV system constructed from Jacobian linearizations at different velocities and slip values. The control problem is formulated as a model-matching control problem within the LPV framework; a specific modification of the LPV control synthesis algorithm is proposed to alleviate controller interpolation problems. Linear and nonlinear simulations indicate that the synthesized controller achieves the required robustness and performance. Copyright © 2008 John Wiley & Sons, Ltd. [source] Network-based H, control for stochastic systemsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 3 2009Xiangyu Meng Abstract This paper investigates the problem of network-based control for stochastic plants. A new model of stochastic time-delay systems is presented where both network-induced delays and packet dropouts are taken into consideration for a sampled-data network-based control system. This model consists of two successive delay components in the state, and we solve the network-based H, control problem based on this model by a new stochastic delay system approach. The controller design for the sampled-data systems is carried out in terms of linear matrix inequalities. Finally, we illustrate the methodology by applying these results to an air vehicle control problem. Copyright © 2008 John Wiley & Sons, Ltd. [source] Integrated fault detection and control for LPV systemsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 3 2009Heng Wang Abstract This paper studies the integrated fault detection and control problem for linear parameter-varying systems. A parameter-dependent detector/controller is designed to generate two signals: residual and control signals that are used to detect faults and simultaneously meet some control objectives. The low-frequency faults and certain finite-frequency disturbances are considered. With the aid of the newly developed linearization techniques, the design methods are presented in terms of solutions to a set of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed methods. Copyright © 2008 John Wiley & Sons, Ltd. [source] Shortest path stochastic control for hybrid electric vehiclesINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 14 2008Edward Dean Tate Jr Abstract When a hybrid electric vehicle (HEV) is certified for emissions and fuel economy, its power management system must be charge sustaining over the drive cycle, meaning that the battery state of charge (SOC) must be at least as high at the end of the test as it was at the beginning of the test. During the test cycle, the power management system is free to vary the battery SOC so as to minimize a weighted combination of fuel consumption and exhaust emissions. This paper argues that shortest path stochastic dynamic programming (SP-SDP) offers a more natural formulation of the optimal control problem associated with the design of the power management system because it allows deviations of battery SOC from a desired setpoint to be penalized only at key off. This method is illustrated on a parallel hybrid electric truck model that had previously been analyzed using infinite-horizon stochastic dynamic programming with discounted future cost. Both formulations of the optimization problem yield a time-invariant causal state-feedback controller that can be directly implemented on the vehicle. The advantages of the shortest path formulation include that a single tuning parameter is needed to trade off fuel economy and emissions versus battery SOC deviation, as compared with two parameters in the discounted, infinite-horizon case, and for the same level of complexity as a discounted future-cost controller, the shortest-path controller demonstrates better fuel and emission minimization while also achieving better SOC control when the vehicle is turned off. Linear programming is used to solve both stochastic dynamic programs. Copyright © 2007 John Wiley & Sons, Ltd. [source] Explicit constructions of global stabilization and nonlinear H, control laws for a class of nonminimum phase nonlinear multivariable systemsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 12 2008Weiyao Lan Abstract This paper investigates a global stabilization problem and a nonlinear H, control problem for a class of nonminimum phase nonlinear multivariable systems. To avoid the complicated recursive design procedure, an asymptotic time-scale and eigenstructure assignment method is adopted to construct the control laws for the stabilization problem and the nonlinear H, control problem. A sufficient solvability condition is established onthe unstable zero dynamics of the system for global stabilization problem and nonlinear H, control problem, respectively. Moreover, based on the sufficient solvability condition, an upper bound of the achievable L2 -gain is estimated for the nonlinear H, control problem. Copyright © 2007 John Wiley & Sons, Ltd. 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