Reliable dissipative control of discrete‐time switched singular systems with mixed time delays and stochastic actuator failures

This study is concerned with the problem of reliable dissipative control for a class of discrete‐time switched singular systems with mixed time delays and multiple actuator failures. The failure probability of each actuator is individually quantified and is governed by an individual random variable satisfying a certain probabilistic distribution in the interval [0, 1]. Attention is focused on identifying a class of slow switching signals and designing a set of reliable mode‐dependent state‐feedback controllers such that, for all admissible mixed time delays and multiple probabilistic actuators faults, the closed‐loop system is stochastically exponentially admissible and strictly (, , ℛ)‐dissipative. By using the Lyapunov function approach and the average dwell‐time scheme, sufficient conditions for the existence of such class of stabilising switching signals and the reliable mode‐dependent controllers are derived in terms of linear matrix inequalities, and the explicit expression for the desired controller gains is also given. A numerical example is given to demonstrate the effectiveness of the theoretical results.