Simultaneous fault detection and controller design for networked-based discrete-time switched systems with time-varying delays

This paper studies the problem of simultaneous fault detection (FD) and control of discrete-time switched systems with time-varying delays under an arbitrary switching signal in a network communication. The missing phenomenon is assumed to occur, in the communication links for sensor-to-controller and controller-to-actuator, where the missing probability of packet dropouts is governed as two different mutually independent Bernoulli distributed white sequences with known conditional probability distributions. The main attention is focused on designing the robust fault detection filter (FDF) such that the estimation error between the residual and fault is minimized in an exponential way and at the same time the closed-loop networked switched system is exponentially stable in the mean-square sense. The simultaneous fault detection and controller design problem is converted into an exponential H-infinity filtering problem. By a multiple Lyapunov-Krasovskii functional (LKF) and the average dwell-time scheme, a novel delay-dependent sufficient conditions are developed to ensure the resulting error system is exponentially stable with an optimized H-infinity disturbance attenuation level. The solution of the parameters of the controllers and fault detection filters is characterized in terms of the feasibility of a convex optimization problem. A numerical example is given to illustrate the effectiveness of the obtained results.