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Jungers M.,University of Lorraine | Castelan E.B.,DAS CTC UFSC | Tarbouriech S.,CNRS | Daafouz J.,University of Lorraine
Nonlinear Analysis: Hybrid Systems | Year: 2011

The paper addresses two control problems of discrete-time switching systems subject to modal nonlinearities satisfying sector conditions, actuator saturations and additive L2-bounded disturbances. Such switching systems consist of a finite family of discrete-time processes that are supervised by logical decision-making algorithms. Conditions based on LMIs are provided for synthesizing the control gains and for obtaining regions of absolute λ-contractivity as large as possible or for obtaining a L2-gain as small as possible. A numerical example illustrates the proposed approaches. © 2010 Elsevier Ltd. Source

Jungers M.,University of Lorraine | Castelan E.B.,DAS CTC UFSC
Systems and Control Letters | Year: 2011

This paper deals with the stabilization of a class of nonlinear discrete-time systems under control saturations including time-varying parameter dependency. The control law studied consists of the gain-scheduled feedback of the measured output and of the nonlinearity present in the dynamics of the controlled system. Furthermore, the saturations are taken into account by modeling the nonlinear saturated system through a dead-zone nonlinearity satisfying a modified sector condition. Thus, as for precisely known systems, linear matrix inequality (LMI) stabilization conditions are proposed for such a generic system. These conditions can be cast into convex programming problems for design purposes. An illustrative example stresses the efficiency of the main result. © 2010 Elsevier B.V. Source

Gomes Da Silva Jr. J.M.,Federal University of Rio Grande do Sul | Castelan E.B.,DAS CTC UFSC | Corso J.,CCT UDESC | Eckhard D.,Federal University of Rio Grande do Sul
Journal of the Franklin Institute | Year: 2013

In the present work a systematic methodology for computing dynamic output stabilizing feedback control laws for nonlinear systems subject to saturating inputs is presented. In particular, the class of Lur'e type nonlinear systems is considered. Based on absolute stability tools and a modified sector condition to take into account input saturation effects, an LMI framework is proposed to design the controller. Asymptotic as well as input-to-state and input-to-output (in a L2 sense) stabilization problems are addressed both in regional (local) and global contexts. The controller structure is composed of a linear part, an anti-windup loop and a term associated to the output of the dynamic nonlinearity. Convex optimization problems are proposed to compute the controller considering different optimization criteria. A numerical example illustrates the potentialities of the methodology. © 2013 The Franklin Institute. Source

Leite V.J.S.,Federal University of Minas Gerais | Castelan E.B.,DAS CTC UFSC | Miranda M.F.,Federal University of Minas Gerais | Viana D.C.,Federal University of Minas Gerais
Proceedings of the 2010 American Control Conference, ACC 2010 | Year: 2010

Convex conditions, proposed as a feasibility test of a set of linear matrix inequalities (LMIs), are given for the design of a partially parameter dependent dynamic output feedback controller for a class of discrete time systems with delayed state. This class concerns the systems with time-varying delay in the state and time varying parameters, both assumed to be available on line. The controller is composed by a classical part, feeding-back the system output and another one where the delayed output of the system is feedback. This last part can be avoided in case of inaccessible delay value, resulting in a more classical control design. Different from other approaches found in the literature, it is used a parameter dependent Lyapunov-Krasovskii functional candidate and a slack matrix variable to reduce the conservatism of the proposed approach. The resulting parameter dependent controller can be obtained on line as a convex combination of some 'vertex' controllers. Numerical examples are presented to illustrated the effectiveness of the proposal. © 2010 AACC. Source

Louis J.,Nancy Research Center for Automatic Control | Jungers M.,Nancy Research Center for Automatic Control | Daafouz J.,Nancy Research Center for Automatic Control | Daafouz J.,Institut Universitaire de France | Castelan E.B.,DAS CTC UFSC
IFAC Proceedings Volumes (IFAC-PapersOnline) | Year: 2015

This paper deals with discrete-time switched Lur'e systems including an additional saturated input and a bounded energy disturbance. Two control design issues are investigated related to the L2-induced gain and the rejection of disturbance. An common optimization problem under LMI conditions and differing from the cost function to optimize, is provided to offer a solution to the both problems. The main approach is to upper bound a criterion with a suitable Lur'e type Lyapunov function. Numerical examples are given to underline the efficiency of our approach and to allow a discussion with the literature. © 2015, IFAC Hosting by Elsevier Ltd. Source

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