Periodically intermittent H_∞ control for discrete‐time switched interval type‐2 fuzzy systems with dwell time constraints: A switching‐path‐dependent Lyapunov function approach

Abstract

This article studies the periodically intermittent control problem of discrete-time switched interval type-2 fuzzy systems (DSIT2FSs) with dwell time constraints.A novel switching-path-dependent Lyapunov functions (SPDLFs) approach, which utilizes the switching path information over multiple controller operation periods, is proposed. First, the N-mode DSIT2FS with periodic intermittent control inputs is regarded as a switched system with N controller-busy modes and N controller-free modes. Then, by constructing a class of non-increasing SPDLFs, sufficient conditions on the existence of H ∞ intermittent interval type-2 (IT2) fuzzy controllers are obtained for DSIT2FS with minimum dwell time constraints. The controller gains can be gotten by solving a set of strict linear matrix inequalities. It is shown that the designed IT2 fuzzy controllers work intermittently but still can guarantee stability and H ∞ performance of the close-loop systems. Finally, two numerical examples are provided to illustrate the effectiveness and advantages of the results. K E Y W O R D Sdiscrete-time switched IT2 fuzzy systems, periodically intermittent H ∞ control, switching-path-dependent Lyapunov function, timer-dependent IT2 fuzzy controller