Robust H control of discrete systems with uncertain parameters and unknown delays

In this paper, we address the problems of robust H"~ performance analysis and control synthesis for a class of discrete-time systems with norm-bounded parameter uncertainty and unknown constant state delay. Through finite-dimensional algebraic Riccati equations, we provide a necessary and sufficient condition for designing a memoryless state-feedback controller which stabilizes the discrete time-delay system under consideration and guarantees an H"~-norm bound constraint on the disturbance attenuation for all admissible uncertainties and unknown delays. An example is worked out to illustrate the developed theory.

[1]  Henryk Górecki,et al.  Analysis and Synthesis of Time Delay Systems , 1989 .

[2]  K. Gu.  H∞ control of systems under norm bounded uncertainties in all system matrices , 1994, IEEE Trans. Autom. Control..

[3]  J. Doyle,et al.  Quadratic stability with real and complex perturbations , 1990 .

[4]  Pin-Lin Liu,et al.  Output feedback stabilization of uncertain dynamic systems with multiple state delays via sliding mode control strategy , 1999, ISIE '99. Proceedings of the IEEE International Symposium on Industrial Electronics (Cat. No.99TH8465).

[5]  B. Anderson,et al.  A first prin-ciples solution to the nonsingular H control problem , 1991 .

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

[7]  Lihua Xie,et al.  H∞ analysis and synthesis of discrete-time systems with time-varying uncertainty , 1993, IEEE Trans. Autom. Control..

[8]  Wassim M. Haddad,et al.  Memoryless H∞ Controllers for Discrete-Time Systems with Time Delay , 1998, Autom..

[9]  E. Verriest,et al.  Robust stability of delay-difference equations , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[10]  Denis Arzelier,et al.  Robust stabilization of discrete-time linear systems with norm-bounded time-varying uncertainty , 1994 .

[11]  Luke E. K. Achenie,et al.  Robust H ∞ control for linear discrete-time systems with norm-bounded time-varying uncertainty , 1996 .

[12]  Magdi S. Mahmoud,et al.  Design of stabilizing controllers for uncertain discrete-time systems with state-delay , 1995 .

[13]  C. D. Souza,et al.  Delay-dependent robust stability and stabilization of uncertain linear delay systems: a linear matrix inequality approach , 1997, IEEE Trans. Autom. Control..

[14]  Lihua Xie,et al.  Output feedback H∞ control of systems with parameter uncertainty , 1996 .

[15]  Lihua Xie,et al.  On the Discrete-time Bounded Real Lemma with application in the characterization of static state feedback H ∞ controllers , 1992 .

[16]  Magdi S. Mahmoud,et al.  Robust control and ltering for time-delay systems , 2002 .

[17]  George A. Perdikaris.  Computer Controlled Systems: Theory and Applications , 1991 .

[18]  Seong-Ho Song,et al.  H∞ Control of discrete-time linear systems with norm-bounded uncertainties and time delay in state , 1998, Autom..