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Robust Stabilization (robust + stabilization)

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Terms modified by Robust Stabilization

  • robust stabilization problem
    		•

    Selected Abstracts

    Robust stabilization of a class of non-minimum-phase nonlinear systems in a generalized output feedback canonical form

    INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 3 2009
    Jun Fu
    Abstract In this paper, a globally robust stabilizer for a class of uncertain non-minimum-phase nonlinear systems in generalized output feedback canonical form is designed. The system contains unknown parameters multiplied by output-dependent nonlinearities and output-dependent nonlinearities enter such a system both additively and multiplicatively. The proposed method relies on a recently developed novel parameter estimator and state observer design methodology together with a combination of backstepping and small-gain approach. Our design has three distinct features. First, the parameter estimator and state observer do not necessarily follow the classical certainty-equivalent principle any more. Second, the design treats unknown parameters and unmeasured states in a unified way. Third, the technique by combining standard backstepping and small-gain theorem ensures robustness with respect to dynamic uncertainties. Finally, two numerical examples are given to show that the proposed method is effective, and that it can be applied to more general systems that do not satisfy the cascading upper diagonal dominance conditions developed in recent papers, respectively. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Robust stabilization for uncertain discrete singular systems with state delay

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 16 2008
    Zhengguang Wu
    Abstract The robust stabilization problem for uncertain discrete singular time-delay systems is addressed in this paper. In terms of strict linear matrix inequality and a finite sum inequality, a delay-dependent criterion for the nominal systems to be admissible is obtained. Based on the criterion, a state feedback controller, which guarantees that, for all admissible uncertainties, the resulting closed-loop system is regular, causal and stable, is constructed. An explicit expression for the desired controller is also given. The obtained results include both delay-independent and delay-dependent cases. Some numerical examples are introduced to show the effectiveness of the given results. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Robust stabilization of a class of uncertain system via block decomposition and VSC

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 15 2002
    Alexander G. Loukianov
    Abstract In this paper, a block decomposition procedure for sliding mode control of a class of nonlinear systems with matched and unmatched uncertainties, is proposed. Based on the nonlinear block control principle, a sliding manifold design problem is divided into a number of sub-problems of lower dimension which can be solved independently. As a result, the nominal parts of the sliding mode dynamics is linearized. A discontinuous feedback is then used to compensate the matched uncertainty. Finally, a step-by-step Lyapunov technique and a high gain approach is applied to obtain hierarchical fast motions on the sliding manifolds and to achieve the robustness property of the closed-loop system motion with respect to unmatched uncertainty. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    Robust stabilization for uncertain discrete singular time-delay systems,

    ASIAN JOURNAL OF CONTROL, Issue 2 2010
    Xiaofu Ji
    Abstract The problem of robust stabilization for uncertain discrete singular time-delay systems is investigated. The considered systems are subject to norm-bounded parameter uncertainties and constant time delay. A linear matrix inequality (LMI) condition is proposed for a discrete singular time-delay system to be regular, causal and stable. With this condition, the problems of robust stability and stabilization are solved. The obtained results are formulated in terms of strict LMIs. An explicit expression of the desired state-feedback control law is also given, which involves no matrix decomposition. The proposed synthesis method is illustrated by a numerical example. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source]

    Delay-dependent robust control for singular discrete-time Markovian jump systems with time-varying delay

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 10 2010
    Wuneng Zhou
    Abstract The problem of delay-dependent robust stabilization for uncertain singular discrete-time systems with Markovian jumping parameters and time-varying delay is investigated. In terms of free-weighting-matrix approach and linear matrix inequalities, a delay-dependent condition is presented to ensure a singular discrete-time system to be regular, causal and stochastically stable based on which the stability analysis and robust stabilization problem are studied. An explicit expression for the desired state-feedback controller is also given. Some numerical examples are provided to demonstrate the effectiveness of the proposed approach. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    Position-dependent disturbance rejection using spatial-based adaptive feedback linearization repetitive control

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 12 2009
    Cheng-Lun Chen
    Abstract In this paper, we propose a new design of spatial-based repetitive control for a class of rotary motion systems operating at variable speeds. The open-loop system in spatial domain is obtained by reformulating a nonlinear time-invariant system with respect to angular displacement. A two-degree-of-freedom control structure (comprising two control modules) is then proposed to robustly stabilize the open-loop system and improve the tracking performance. The first control module applies adaptive feedback linearization with projected parametric update and concentrates on robust stabilization of the closed-loop system. The second control module introduces a spatial-based repetitive controller cascaded with a loop-shaping filter, which not only further reduces the tracking error, but also improves parametric adaptation. The overall control system is robust to model uncertainties of the system and capable of rejecting position-dependent disturbances under varying process speeds. Stability proof for the overall system is given. A design example with simulation is provided to demonstrate the applicability of the proposed design. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Robust H, control of uncertain linear impulsive stochastic systems

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 13 2008
    Wu-Hua Chen
    Abstract This paper develops robust stability theorems and robust H, control theory for uncertain impulsive stochastic systems. The parametric uncertainties are assumed to be time varying and norm bounded. Impulsive stochastic systems can be divided into three cases, namely, the systems with stable/stabilizable continuous-time stochastic dynamics and unstable/unstabilizable discrete-time dynamics, the systems with unstable/unstabilizable continuous dynamics and stable/stabilizable discrete-time dynamics, and the systems in which both the continuous-time stochastic dynamics and the discrete-time dynamics are stable/stabilizable. Sufficient conditions for robust exponential stability and robust stabilization for uncertain impulsive stochastic systems are derived in terms of an average dwell-time condition. Then, a linear matrix inequality-based approach to the design of a robust H, controller for each system is presented. Finally, the numerical examples are provided to demonstrate the effectiveness of the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    Polynomial control: past, present, and future

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 8 2007
    Vladimír Ku
    Abstract Polynomial techniques have made important contributions to systems and control theory. Engineers in industry often find polynomial and frequency domain methods easier to use than state equation-based techniques. Control theorists show that results obtained in isolation using either approach are in fact closely related. Polynomial system description provides input,output models for linear systems with rational transfer functions. These models display two important system properties, namely poles and zeros, in a transparent manner. A performance specification in terms of polynomials is natural in many situations; see pole allocation techniques. A specific control system design technique, called polynomial equation approach, was developed in the 1960s and 1970s. The distinguishing feature of this technique is a reduction of controller synthesis to a solution of linear polynomial equations of a specific (Diophantine or Bézout) type. In most cases, control systems are designed to be stable and meet additional specifications, such as optimality and robustness. It is therefore natural to design the systems step by step: stabilization first, then the additional specifications each at a time. For this it is obviously necessary to have any and all solutions of the current step available before proceeding any further. This motivates the need for a parametrization of all controllers that stabilize a given plant. In fact this result has become a key tool for the sequential design paradigm. The additional specifications are met by selecting an appropriate parameter. This is simple, systematic, and transparent. However, the strategy suffers from an excessive grow of the controller order. This article is a guided tour through the polynomial control system design. The origins of the parametrization of stabilizing controllers, called Youla,Ku,era parametrization, are explained. Standard results on reference tracking, disturbance elimination, pole placement, deadbeat control, H2 control, l1 control and robust stabilization are summarized. New and exciting applications of the Youla,Ku,era parametrization are then discussed: stabilization subject to input constraints, output overshoot reduction, and fixed-order stabilizing controller design. Copyright © 2006 John Wiley & Sons, Ltd. [source]

    Global robust stabilization of nonlinear systems subject to input constraints

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 14 2002
    Rodolfo Suárez
    Abstract Our main purpose in this paper is to further address the global stabilization problem for affine systems by means of bounded feedback control functions, taking into account a large class of control value sets: p,r -weighted balls ,mr(p), with 10 are also considered. Working along the line of Artstein,Sontag's approach, we construct an explicit formula for a one-parameterized family of continuous feedback controls taking values in ,rm(p) that globally asymptotically stabilize an affine system, provided an appropriate control Lyapunov function is known. The designed family of controls is suboptimal with respect to the robust stability margin for uncertain systems. The problem of achieving disturbance attenuation for persistent disturbances is also considered. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    Adaptive robust stabilization of dynamic nonholonomic chained systems

    JOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 3 2001
    S. S. Ge
    In this article, the stabilization problem is investigated for dynamic nonholonomic systems with unknown inertia parameters and disturbances. First, to facilitate control system design, the nonholonomic kinematic subsystem is transformed into a skew-symmetric form and the properties of the overall systems are discussed. Then, a robust adaptive controller is presented in which adaptive control techniques are used to compensate for the parametric uncertainties and sliding mode control is used to suppress the bounded disturbances. The controller guarantees the outputs of the dynamic subsystem (the inputs to the kinematic subsystem) to track some bounded auxiliary signals which subsequently drive the kinematic subsystem to the origin. In addition, it can also be shown all the signals in the closed loop are bounded. Simulation studies on the control of a unicycle wheeled mobile robot are used to show the effectiveness of the proposed scheme. © 2001 John Wiley & Sons, Inc. [source]

    Robust H, control of stochastic time-delay jumping systems with nonlinear disturbances

    OPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 5 2006
    Guoliang Wei
    Abstract This paper deals with the problems of robust stabilization and H, control for a class of uncertain stochastic jumping systems with nonlinear disturbances and time delays. The uncertain parameters are assumed to be norm-bounded and mode dependent, and the time delays enter into the state matrix, the stochastic perturbation term, as well as the state feedback. The stochastic robust stabilization problem addressed in this paper is to design a state feedback controller with input delay such that, for all admissible uncertainties and the nonlinear disturbances, the closed-loop system is robustly, stochastically, exponentially stable in the mean square. Moreover, the purpose of the robust H, control problem is to guarantee a specified H, performance index, while still achieving the mean-square exponential stability requirement for the closed-loop system. By resorting to the Itô's differential formula and the Lyapunov stability theory, sufficient conditions are derived, respectively, for the robust stabilization and the robust H, control problems. It is shown that the addressed problems can be solved if a set of linear matrix inequalities (LMIs) are feasible. A numerical example is employed to illustrate the usefulness of the proposed LMI-based design methods. Copyright © 2006 John Wiley & Sons, Ltd. [source]

    Robust stabilization for uncertain discrete singular time-delay systems,

    ASIAN JOURNAL OF CONTROL, Issue 2 2010
    Xiaofu Ji
    Abstract The problem of robust stabilization for uncertain discrete singular time-delay systems is investigated. The considered systems are subject to norm-bounded parameter uncertainties and constant time delay. A linear matrix inequality (LMI) condition is proposed for a discrete singular time-delay system to be regular, causal and stable. With this condition, the problems of robust stability and stabilization are solved. The obtained results are formulated in terms of strict LMIs. An explicit expression of the desired state-feedback control law is also given, which involves no matrix decomposition. The proposed synthesis method is illustrated by a numerical example. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source]

    Delay-dependent robust stabilization for uncertain stochastic switching systems with distributed delays,

    ASIAN JOURNAL OF CONTROL, Issue 5 2009
    Hao Shen
    Abstract This paper deals with the problem of robust stabilization for a class of uncertain stochastic switching systems with distributed delays. The purpose is to design a memory controller, which guarantees that the resulting closed-loop system is mean-square asymptotically stable. In terms of a set of linear matrix inequalities, a delay-dependent condition is proposed and a robust memory controller is designed. Two numerical examples are provided to illustrate the effectiveness of the proposed method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source]

    Delay-dependent robust stability and stabilization for uncertain discrete singular systems with delays ,,

    ASIAN JOURNAL OF CONTROL, Issue 3 2009
    Shuping Ma
    Abstract The robust stability and robust stabilization for time-delay discrete singular systems with parameter uncertainties is discussed. A delay-dependent linear matrix inequality (LMI) condition for the time-delay discrete systems to be nonsingular and stable is given. Based on this condition and the restricted system equivalent transformation, the delay-dependent LMI condition is proposed for the time-delay discrete singular systems to be admissible. With this condition, the problems of robust stability and robust stabilization are solved, and the delay-dependent LMI conditions are obtained. Numerical examples illustrate the effectiveness of the method given in the paper. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source]

    ROBUST STABILITY AND STABILIZATION OF A CLASS OF SINGULAR SYSTEMS WITH MULTIPLE TIME-VARYING DELAYS

    ASIAN JOURNAL OF CONTROL, Issue 1 2006
    S. M. Saadni
    ABSTRACT This paper deals with the problem of robust stability and robust stabilization for uncertain continuous singular systems with multiple time-varying delays. The parametric uncertainty is assumed to be norm bounded. The purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular, impulse free, and stable for all admissible uncertainties. The purpose of the robust stabilization problem is to design a feedback control law such that the resulting closed-loop system is robustly stable. This problem is solved via generalized quadratic stability approach. A strict linear matrix inequality (LMI) design approach is developed. Finally, a numerical example is provided to demonstrate the application of the proposed method. [source]

    GENERALIZED QUADRATIC STABILIZATION FOR DISCRETE-TIME SINGULAR SYSTEMS WITH TIME-DELAY AND NONLINEAR PERTURBATION

    ASIAN JOURNAL OF CONTROL, Issue 3 2005
    Guoping Lu
    ABSTRACT This paper discusses a generalized quadratic stabilization problem for a class of discrete-time singular systems with time-delay and nonlinear perturbation (DSSDP), which the satisfies Lipschitz condition. By means of the S-procedure approach, necessary and sufficient conditions are presented via a matrix inequality such that the control system is generalized quadratically stabilizable. An explicit expression of the static state feedback controllers is obtained via some free choices of parameters. It is shown in this paper that generalized quadratic stability also implies exponential stability for linear discrete-time singular systems or more generally, DSSDP. In addition, this new approach for discrete singular systems (DSS) is developed in order to cast the problem as a convex optimization involving linear matrix inequalities (LMIs), such that the controller can stabilize the overall system. This approach provides generalized quadratic stabilization for uncertain DSS and also extends the existing robust stabilization results for non-singular discrete systems with perturbation. The approach is illustrated here by means of numerical examples. [source]

    IMPROVED CONDITIONS FOR DELAY-DEPENDENT ROBUST STABILITY AND STABILIZATION OF UNCERTAIN DISCRETE TIME-DELAY SYSTEMS

    ASIAN JOURNAL OF CONTROL, Issue 3 2005
    Shengyuan Xu
    ABSTRACT This paper provides improved delay-dependent conditions for the robust stability and robust stabilization of discrete time-delay systems with norm-bounded parameter uncertainties. It is theoretically established that the proposed conditions are less conservative than those discussed in the literature. The new approach proposed in this paper in a derivation of delay-dependent conditions and involves the use of neither model transformation nor bounding techniques for some cross terms. A numerical example is provided to demonstrate the reduced conservatism of the proposed conditions. [source]

    A NEW DESIGN APPROACH TO DELAY-DEPENDENT ROBUST H, CONTROL FOR UNCERTAIN TIME-DELAY SYSTEMS

    ASIAN JOURNAL OF CONTROL, Issue 4 2004
    Ning-Jun Su
    ABSTRACT A new design approach to delay-dependent robust stabilization and robust H, control for a class of uncertain time-delay systems is provided in this paper. The sufficient conditions for delay-dependent robust stabilization and robust H, control are derived based on a new state transformation and given in terms of linear matrix inequalities (LMI). Numerical examples are presented to show that the proposed results can be less conservative and can be used to deal with not only small but also large delay systems. [source]

    Output Feedback Sliding Mode Controller Design Via H, THEORY

    ASIAN JOURNAL OF CONTROL, Issue 1 2003
    Jeang-Lin Chang
    ABSTRACT For a linear system with mismatched disturbances, a sliding mode controller using only output feedback is developed in this paper. Through application of the H, control theory, the designed switching surface can achieve robust stabilization and guarantee a level of disturbance rejection during sliding mode. Although the system exhibits disturbances, a state estimator is used which, using only measured outputs, can asymptotically estimate the system states. The control law is designed with respect to the estimated signals. Finally, a numerical example is presented to demonstrate the proposed control scheme. [source]