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LMI Constraints (lmi + constraint)
Selected AbstractsOn delay-dependent LMI-based guaranteed cost control of uncertain neutral systems with discrete and distributed time-varying delaysINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 12 2007Jenq-Der Chen Abstract In this paper, the problem of designing robust guaranteed cost control law for a class of uncertain neutral system with a given quadratic cost function is considered. Based on Lyapunov,Krasovskii functional theory, a delay-dependent criterion for the existence of guaranteed cost controller is expressed in the form of two linear matrix inequalities (LMIs), which can be solved by using effective LMI toolbox. Moreover, a convex optimization problem satisfying some LMI constraints is formulated to solve a guaranteed cost controller which achieves the minimization of the closed-loop guaranteed cost. An efficient approach is proposed to design the guaranteed cost control for uncertain neutral systems. Computer software Matlab can be used to solve all the proposed results. Finally, a numerical example is illustrated to show the usefulness of our obtained design method. Copyright © 2006 John Wiley & Sons, Ltd. [source] Delay-dependent anti-windup strategy for linear systems with saturating inputs and delayed outputsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 7 2004S. Tarbouriech Abstract This paper addresses the problem of the determination of stability regions for linear systems with delayed outputs and subject to input saturation, through anti-windup strategies. A method for synthesizing anti-windup gains aiming at maximizing a region of admissible states, for which the closed-loop asymptotic stability and the given controlled output constraints are respected, is proposed. Based on the modelling of the closed-loop system resulting from the controller plus the anti-windup loop as a linear time-delay system with a dead-zone nonlinearity, constructive delay-dependent stability conditions are formulated by using both quadratic and Lure Lyapunov,Krasovskii functionals. Numerical procedures based on the solution of some convex optimization problems with LMI constraints are proposed for computing the anti-windup gain that leads to the maximization of an associated stability region. The effectiveness of the proposed technique is illustrated by some numerical examples. Copyright © 2004 John Wiley & Sons, Ltd. [source] Fixed-order H, control design via a partially augmented Lagrangian methodINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 12 2003Pierre Apkarian Abstract In this paper we develop an augmented Lagrangian method to determine local optimal solutions of the reduced- and fixed-order H, synthesis problems. We cast these synthesis problems as optimization programs with a linear cost subject to linear matrix inequality (LMI) constraints along with nonlinear equality constraints representing a matrix inversion condition. The special feature of our algorithm is that only equality constraints are included in the augmented Lagrangian, while LMI constraints are kept explicitly in order to exploit currently available semi definite programming (SDP) codes. The step computation in the tangent problem is based on a Gauss,Newton model, and a specific line search and a first-order Lagrange multiplier update rule are used to enhance efficiency. A number of computational results are reported and underline the strong practical performance of the algorithm. Copyright © 2003 John Wiley & Sons, Ltd. [source] ,2 suboptimal estimation and control for nonnegative dynamical systemsOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 1 2009Wassim M. Haddad Abstract Linear matrix inequalities (LMIs) provide a powerful design framework for linear control problems. In this paper, we use LMIs to develop ,2 (sub)optimal estimators and controllers for nonnegative dynamical systems. Specifically, we formulate a series of generalized eigenvalue problems subject to a set of LMI constraints for designing ,2 suboptimal estimators, static controllers, and dynamic controllers for nonnegative dynamical systems. The resulting ,2 suboptimal controllers guarantee that the closed-loop plant system states remain in the nonnegative orthant of the state space. Finally, a numerical example is provided to demonstrate the efficacy of the proposed approach. Copyright © 2008 John Wiley & Sons, Ltd. [source] ,, model reduction for uncertain two-dimensional discrete systemsOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 4 2005Huijun Gao Abstract This paper investigates the problem of ,, model reduction for two-dimensional (2-D) discrete systems with parameter uncertainties residing in a polytope. For a given robustly stable system, our attention is focused on the construction of a reduced-order model, which also resides in a polytope and approximates the original system well in an ,, norm sense. Both Fornasini,Marchesini local state-space (FMLSS) and Roesser models are considered through parameter-dependent approaches, with sufficient conditions obtained for the existence of admissible reduced-order solutions. Since these obtained conditions are not expressed as strict linear matrix inequalities (LMIs), the cone complementary linearization method is exploited to cast them into sequential minimization problems subject to LMI constraints, which can be readily solved using standard numerical software. In addition, the development of zeroth order models is also presented. Two numerical examples are provided to show the effectiveness of the proposed theories. Copyright © 2005 John Wiley & Sons, Ltd. [source] | ||||||||||