Robust disturbance attenuation for discrete‐time active fault tolerant control systems with uncertainties

Abstract

SUMMARYThe problems of stochastic stability and stochastic disturbance attenuation for a class of linear discretetime systems are considered in this paper. The system under study is a state space model possessing two Markovian jump parameters: one is failure process and another is failure detection and isolation scheme. A controller is designed to guarantee the stochastic stability and a disturbance attenuation level. Robustness problems for the above system with norm-bounded parameter uncertainties are also investigated. It is shown that the uncertain system can be robustly stochastically stabilized and have a robust disturbance attenuation level for all admissible perturbations if a set of coupled Riccati inequalities has solutions. A numerical example is given to show the potential of the proposed technique.

Output feedback stochastic H∞ stabilization of networked fault-tolerant control systems

“…stochastic stabilization) of the system (4) is now changed to a problem of finding a global solution of the minimization problem (24) (resp. (25)). This is however, still a difficult issue since the objective function is nonconvexe.…”

“…The theory of stability, optimal control and H 2 /H ∞ control, as well as important applications of such systems, can be found in several papers in the current literature, for instance in [5,6,7,8,10,12,13,14,15,18,19] for continuous-time case, and [9] for the discrete-time case. Fault tolerant control issues were also considered in the same framework, for instance in [1,2,3,22,24,25,26].…”

Stabilization of active fault‐tolerant control systems by uncertain nonhomogeneous markovian jump models

“…Many researchers have studied AFTCSs modeled by two Markov processes. Stability and stabilization of such systems are investigated in [39], robust controllers are designed at [10,[40][41][42][43] and optimal control strategies are proposed in [44]. Although the AFTCS provided by the aforementioned studies [10,[39][40][41][42][43][44] seem to be applicable, but they are based on FDD chains with complete information on transition rate (TR) entries, which is a very restrictive and idealistic assumption from the practical point of view.…”

Asymptotic stability in the distribution of nonlinear stochastic systems with semi-Markovian switching

“…For some representative work on this general topic, we refer the reader to [1][2][3][4][5][7][8][9][10][13][14][15]17] and the references therein. Some recent results can be found in [16,18,19]. Because the sojourn time at any state of a Markov chain is exponential, Markovian switchings have limited applications, and the results obtained for these systems are conservative in some sense.…”