Sliding mode parameter adjustment for perturbed linear systems with actuators via invariant ellipsoid method

A methodology for the design of sliding mode controllers for perturbed quasi-linear systems in the presence of actuators is presented. This technique is based on the invariant ellipsoid method and given in terms of the solution of a set of linear matrix inequalities. The provided methodology allows the design of the controller parameters ensuring global convergence of the states to a suboptimal ellipsoidal region around the origin even in the presence of both matched and unmatched uncertainties/disturbances. A benchmark example illustrates a good workability of the suggested technique. Copyright © 2010 John Wiley & Sons, Ltd.

[1]  Leonid M. Fridman,et al.  Singularly perturbed analysis of chattering in relay control systems , 2002, IEEE Trans. Autom. Control..

[2]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[3]  Boris T. Polyak,et al.  Rejection of bounded exogenous disturbances by the method of invariant ellipsoids , 2007 .

[4]  S. Żak,et al.  Robust output feedback stabilization of uncertain dynamic systems with bounded controllers , 1993 .

[5]  Vadim I. Utkin,et al.  Sliding mode control in electromechanical systems , 1999 .

[6]  Christopher Edwards,et al.  Sliding mode control : theory and applications , 1998 .

[7]  Vadim I. Utkin,et al.  Sliding Modes in Control and Optimization , 1992, Communications and Control Engineering Series.

[8]  Han Ho Choi,et al.  Variable structure output feedback control design for a class of uncertain dynamic systems , 2002, Autom..

[9]  Boris T. Polyak,et al.  Suppression of bounded exogenous disturbances: Output feedback , 2008 .

[10]  Leonid M. Fridman,et al.  Analysis and design of integral sliding manifolds for systems with unmatched perturbations , 2006, IEEE Transactions on Automatic Control.

[11]  Leonid M. Fridman,et al.  An averaging approach to chattering , 2001, IEEE Trans. Autom. Control..

[12]  A. Kurzhanski,et al.  Ellipsoidal Calculus for Estimation and Control , 1996 .

[13]  Han Ho Choi.  Sliding-Mode Output Feedback Control Design , 2008, IEEE Transactions on Industrial Electronics.

[14]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[15]  Alexander S. Poznyak,et al.  Minimization of the unmatched disturbances in the sliding mode control systems via invariant ellipsoid method , 2009, 2009 IEEE Control Applications, (CCA) & Intelligent Control, (ISIC).

[16]  Liu Hsu,et al.  MODEL-REFERENCE OUTPUT-FEEDBACK SLIDING MODE CONTROLLER FOR A CLASS OF MULTIVARIABLE NONLINEAR SYSTEMS , 2008 .

[17]  Marcelo C. M. Teixeira,et al.  Variable-Structure Control Design of Switched Systems With an Application to a DC–DC Power Converter , 2009, IEEE Transactions on Industrial Electronics.

[18]  Christopher Edwards,et al.  Sliding-Mode Output-Feedback Control Based on LMIs for Plants With Mismatched Uncertainties , 2009, IEEE Transactions on Industrial Electronics.

[19]  Franco Blanchini,et al.  Set invariance in control , 1999, Autom..

[20]  Ji Xiang,et al.  An ILMI approach to robust static output feedback sliding mode control , 2006 .