Stability analysis of discrete-time fuzzy positive systems with time delays

Abstract

This paper addresses stability analysis for fuzzy positive systems with time delays represented by Takagi-Sugeno type models. Based on the fuzzy linear Lyapunov functions or functionals, we give stability conditions for fuzzy positive systems with constant time delays. Based on the so-called solution trajectory approach, we give stability conditions for fuzzy positive systems with time-varying delays. All the stability results are delay independent and formulated as linear programmings (LPs) or linear matrix inequalities (LMIs) that are numerically feasible. This paper also discusses the conservatism for these different approaches. Moreover, this paper proposes some necessary conditions of stability for fuzzy positive systems with time delays.