Stochastic stability of fault tolerant control systems with model uncertainties

In this paper, the stochastic stability of fault tolerant control systems (FTCS) in the presence of modeling uncertainties and noise has been studied using Lyapunov function approach. In particular, FTCS with Markovian parameters in the presence of white Gaussian noise and unknown time-varying but bounded uncertainties are considered. Testable necessary and sufficient conditions for the exponential stability in the mean square are derived. A numerical example is presented to demonstrate the theory.

[1]  D. Sworder.  Feedback control of a class of linear systems with jump parameters , 1969 .

[2]  W. Wonham.  Random differential equations in control theory , 1970 .

[3]  M. Mariton,et al.  Robust jump linear quadratic control: A mode stabilizing solution , 1985 .

[4]  I. Petersen.  A stabilization algorithm for a class of uncertain linear systems , 1987 .

[5]  David Vlack,et al.  Robust Control , 1987 .

[6]  A. Haurie,et al.  Optimality conditions for continuous time systems with controlled jump Markov disturbances: application to an FMS planning problem , 1988 .

[7]  H. Chizeck,et al.  Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control , 1990 .

[8]  K. Loparo,et al.  Stochastic stability properties of jump linear systems , 1992 .

[9]  R. Srichander,et al.  Stochastic stability analysis for continuous-time fault tolerant control systems , 1993 .

[10]  P. Shi.  Robust Control for Linear Systems with Markovian Jumping Parameters , 1996 .

[11]  E. Boukas,et al.  On stabilization of uncertain linear systems with jump parameters , 1999 .

[12]  Youmin Zhang,et al.  Analysis of the stochastic stability for fault tolerant control systems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[13]  David D. Sworder,et al.  Control of linear jump systems in noise , 1999, Autom..

[14]  M. Mahmoud,et al.  Stochastic stability of fault tolerant control systems in the presence of noise , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).