Delay-dependent fault detection for switched linear systems with time-varying delays—the average dwell time approach

In this paper, the fault detection problem is investigated for a class of discrete-time switched linear systems with time-varying delays. The main purpose is to design a fault detection filter such that, for all unknown inputs, control inputs and time delays, the estimation error between the residual and fault is minimized in an exponential way. The fault detection problem is converted into an exponential H∞ filtering problem. By using a newly constructed Lyapunov functional and the average dwell time scheme, a novel delay-dependent sufficient condition for the solvability of this problem is established in terms of linear matrix inequalities (LMIs). A numerical example is given to demonstrate the effectiveness of the developed theoretical results.