Robust reliable control for a class of time-varying uncertain impulsive systems

Abstract

The problem of robust and reliable control design for linear uncertain impulsive systems with both time-varying norm-bounded parameter uncertainty and actuator failures was studied. The actuators are classified into two groups. One set of actuators susceptible to failures is possible to fail, the other set of actuators robust to failures is assumed never to fail. The outputs of the actuator failures are regarded as zero. The purpose is to design the state feedback controller such that, for all admissible uncertainties as well as actuator failures occurring among a prespecified subset of actuators, the plant remains asymptotically stable. A modified algebraic Riccati equation approach was developed to solve the problem addressed and a robust reliable control law was obtained. An numerical example was also offered to prove the effectiveness of the proposed method.

Keywords

reliable control / uncertain impulsive systems / state feedback / stabilization

References

[1] VeilletteR JReliable stable feedback and reliable observers[A], 1992, Tucson, AZ: 2898-2903

[2] VeilletteR J, MedanicJ V, PerkinsW R. Design of reliable control systems[J]. IEEE Trans Autom Control, 1992, 37: 290-304

[3] SeoC J, KimB K. Robust and reliable H_∞ control for linear systems with parameter uncertainty and actuator failure[J]. Automatica, 1996, 32: 465-467

[4] WangZi-dong, HuangBiao, UnbehauenH. Robust reliable control for a class of uncertain nonlinear state-delayed system[J]. Automatica, 1999, 35: 955-963

[5] LiuX Z. Stability results for impulsive differential systems with applications to population growth models [J]. Dynamics and Stability of Systems, 1994, 9: 163-174

[6] LakshmikanthamV, BainovD D, SimeonovP STheory of Impulsive Differential Equations[M], 1989, Singapore, World Scientific

[7] LakshmikanthamV, LiuX ZStability Analysis in Terms of Two Measures[M], 1989, Singapore, World Scientific

[8] LiuX Z. Practical stabilization of control systems with impulse effects[J]. Journal of Mathematical Analysis and Application, 1992, 166: 563-576

[9] LiuX Z, BallingerG. Uniform asymptotic stability of impulsive delay differential equations[J]. Computers and Mathematics with Application, 2001, 41: 903-915

[10] YeH. Stability analysis of systems with impulse effects[J]. IEEE Trans Automat Contr, 1997, 44: 976-988

[11] YeH, MichelA N, HouL. Stability analysis of systems with impulsive effects[J]. IEEE Trans Autom Contr, 1998, 43: 1719-1723

[12] ChengXin-ming, GuanZhi-hong, LiuXin-zhi. Decentralized impulsive control for a class of uncertain interconnected systems[J]. Journal of Zhejiang University Science, 2004, 5: 274-282