CONTROL LAW FOR QUADRATIC STABILIZATION OF PERTURBED FUZZY TIME‐DELAY LARGE‐SCALE SYSTEMS VIA LMI

Abstract

ABSTRACTIn this paper, the perturbed continuous‐time large‐scale system with time delays is represented by an equivalent Takagi‐Sugeno type fuzzy model. First, two types of decentralized state feedback controllers are considered in this paper. Based on the Riccati‐type inequality, the Razumikhin theorem, and the delay‐dependent Lyapunov functional approach, some controller design approaches are proposed to stabilize the whole fuzzy time‐delay system asymptotically. In these design methods, both the delay‐independent and delay‐dependent stabilization criteria are derived. By Schur complement, these sufficient conditions can be easily transformed into the problem of LMI's. Moreover, the systems with all the time‐delays τlij (t) are the same for all rules (i.e., τlij (t) = τmij (t) = τij for all l =m); the authors also propose a simpler and less conservative stabilizing criteria. A numerical example is given to illustrate the control design and its effectiveness.