Model Approximation for Fuzzy Switched Systems With Stochastic Perturbation

• Published in: IEEE transactions on fuzzy systems Vol. 23; no. 5; pp. 1458 - 1473
• Main Authors: Xiaojie Su, Ligang Wu, Peng Shi, Chen, C. L. Philip
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.10.2015; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Approximation; Approximation methods; Educational institutions; Errors; Fuzzy; Fuzzy logic; Fuzzy set theory; Fuzzy systems; Hankel-norm performance; Mathematical analysis; model approximation; Reduced order systems; Stochastic processes; Stochastic systems; Stochasticity; Switched systems; Switches; stochastic systems; model approximation; switched systems; Hankel-norm performance; Fuzzy systems
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2014.2362153

In this paper, the model approximation problem is investigated for a Takagi-Sugeno fuzzy switched system with stochastic disturbance. For a high-order considered system, our attention is focused on the construction of a reduced-order model, which not only approximates the original system well with a Hankel-norm performance but translates it into a lower dimensional fuzzy switched system as well. By using the average dwell time approach and the piecewise Lyapunov function technique, a sufficient condition is first proposed to guarantee the mean-square exponential stability with a Hankel-norm error performance for the error system. The model approximation is then converted into a convex optimization problem by using a linearization procedure. Finally, simulations are provided to illustrate the effectiveness of the proposed theory.