Resilient control of non-linear discrete-time state-delay systems

A class of non-linear discrete-time systems with state-delay is considered. We develop an LMI-based analysis and design procedures to check primarily into the robust stability of discrete-time systems with state-delay and bounded non-linearities. Then we address the robust stabilization using nominal and resilient feedback designs. In both cases the trade-off between the size of the controller gains and the bounding factors is illuminated and incorporated into the design formalism. Seeking computational convenience, all the developed results are cast in the format of linear matrix inequalities (LMIs) and several numerical examples are presented throughout the paper to illustrate the feasibility of the theoretical developments.

[1]  Magdi S. Mahmoud,et al.  Robust H control of discrete systems with uncertain parameters and unknown delays , 2000, Autom..

[2]  Magdi S. Mahmoud,et al.  Resilient control of uncertain dynamical systems , 2003 .

[3]  Peng Shi,et al.  Resilient feedback stabilization of discrete-time systems with delays , 2008, IMA J. Math. Control. Inf..

[4]  M. Mahmoud,et al.  H∞-Controllers for Time-Delay Systems Using Linear Matrix Inequalities , 1999 .

[5]  El-Kébir Boukas,et al.  Robust control and filtering for time‐delay systems, M. S. Mahmoud, Marcel Dekker, New York, 2000. ISBN 0‐8247‐0327‐8 , 2001 .

[6]  E. Yaz Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[7]  Magdi S. Mahmoud,et al.  New results on robust control design of discrete-time uncertain systems , 2005 .

[8]  Jianliang Wang,et al.  Non-fragile Hinfinity control for linear systems with multiplicative controller gain variations , 2001, Autom..

[9]  Joseph R. Corrado,et al.  Robust resilient dynamic controllers for systems with parametric uncertainty and controller gain variations , 2000 .

[10]  Vladimir Bobal,et al.  Design of Robust Controllers for Time-Delay Systems , 1997 .

[11]  Magdi S. Mahmoud,et al.  Robust performance results for discrete-time systems , 1998 .

[12]  E. Boukas,et al.  DELAY-DEPENDENT STABILIZATION OF SINGULAR LINEAR SYSTEMS WITH DELAYS , 2006 .

[13]  P. Dorato,et al.  Non-fragile controller design: an overview , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[14]  Guang-Hong Yang,et al.  H8 control for linear systems with additive controller gain variations , 2000 .

[15]  Magdi S. Mahmoud Linear parameter-varying discrete time-delay systems: Stability and l 2-gain controllers , 2000 .

[16]  El-Kébir Boukas Singular linear systems with delay: ℋ︁∞ stabilization , 2007 .

[17]  G. M. Bahaa Optimal control for cooperative parabolic systems governed by Schrödinger operator with control constraints , 2007, IMA J. Math. Control. Inf..

[18]  M. Mahmoud Robust Control and Filtering for Time-Delay Systems , 2000 .

[19]  Wei Wang,et al.  TWO DESIGN SCHEMES FOR ROBUST ADAPTIVE CONTROL OF A CLASS OF LINEAR UNCERTAIN NEUTRAL DELAY SYSTEMS , 2007 .

[20]  Yan Shi,et al.  Resilient observer-based control of uncertain time-delay systems , 2007 .

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