Abstract
This paper investigates the asymptotic stability of a class of TS fuzzy switched systems when an arbitrary switching strategy is adopted. The proposed method, applied to neutral and retarded-type systems, is based on the vector-norms approach. The idea consists in defining a common comparison system to all the fuzzy models. If this comparison system can be described by a state matrix that fulfills the properties of the opposite of an M-matrix, then we can conclude on the asymptotic stability of the initial system via simple algebraic delay-independent conditions.
Highlights
Switched systems are defined as an important class of hybrid dynamical systems that consists of several continuous-time or discrete-time subsystems
Besides and during the past decades, fuzzy theory about modeling and control and more about TakagiSugeno (TS) fuzzy models has been recognized as a powerful approximation tool when dealing with complex and illdetermined systems [3,4,5,6]
Lyapunov theory has been at the origin of most of the results on stability of TS fuzzy switched time-delay systems under arbitrary switching strategy
Summary
Switched systems are defined as an important class of hybrid dynamical systems that consists of several continuous-time or discrete-time subsystems. Lyapunov theory has been at the origin of most of the results on stability of TS fuzzy switched time-delay systems under arbitrary switching strategy. In the case of TS fuzzy neutral or retarded time-delay switched systems, finding a common Lyapunov-Krasovskii functional for all the fuzzy models is a hard task. We propose to study the stability of TS fuzzy switched time-delay systems under arbitrary switching via the vector-norms approach as an alternative to the Lyapunov method [17,18,19]. 2. Neutral-Type TS Fuzzy Switched Time-Delay Systems Described by Functional Differential Equations. The neutral-type time-delay switched system is described by the following state space representation:. Relations (60) and (63) are considered useful when the common comparison system is identical to one of the fuzzy models
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