Robust fuzzy stabilization of nonlinear time-delay systems subject to impulsive perturbations

• Published in: Communications in nonlinear science & numerical simulation Vol. 80; p. 104953
• Main Authors: Zhang, Jinsen, Chen, Wu-Hua, Lu, Xiaomei
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.01.2020; Elsevier Science Ltd
• Subjects: Fuzzy logic; Fuzzy systems; Impulse-time-dependent Lyapunov function; Impulsive perturbations; Liapunov functions; Linear matrix inequalities; Lower bounds; Mathematical analysis; Mathematical functions; Mathematical models; Matrix methods; Nonlinear systems; PDC control; Robust stabilization; Robustness (mathematics); Stability criteria; Systems stability; Takagi–Sugeno (T-S) fuzzy time-delay systems; Time delay systems; Time dependence; Impulsive perturbations; Takagi–Sugeno (T-S) fuzzy time-delay systems; PDC control; Impulse-time-dependent Lyapunov function
• DOI: 10.1016/j.cnsns.2019.104953
• ISSN: 1007-5704

•New analysis and design methods based on the use of impulse-time-dependent Lyapunov function/functional are proposed.•The restrictive condition on the relationship between the size of time-delay and lower bound of impulse intervals imposed by the previous results is removed.•The fuzzy PDC control design methodology for both cases of fast and slow time-varying delay is developed. This paper is concerned with robust stabilization problem of Takagi–Sugeno (T-S) fuzzy time-delay systems subject to impulsive perturbations. New results on robust stabilization via parallel distributed compensation (PDC) control are derived. First, based on the impulse-type Razumikhin–Lyapunov method combined with the use of an impulse-time-dependent Lyapunov function, a new exponential stability criterion for T-S fuzzy time-delay system with impulsive effects is obtained. The proposed stability criterion removes the restrictive condition on the relationship between the size of time-delay and lower bound of impulse intervals imposed by the previous results. Then, by employing a convex relaxation technique, a sufficient condition for the constructing the PDC controllers is presented, which is expressed in terms of linear matrix inequalities (LMIs). Next, the robust stabilization problem for the T-S system with slowly time-varying delay is studied. A different stabilization condition is derived via an impulse-time-dependent Lyapunov functional, which is less conservative than the former when the state delay is constant. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed analysis and design techniques.