Stability analysis and H∞ control of discrete T–S fuzzy hyperbolic systems

• Main Authors: Duan Ruirui, Li Junmin, Zhang Yanni, Yang Ying, Chen Guopei
• Format: Article
• Language: English
• Published: Sciendo 2016-03-01
• Series: International Journal of Applied Mathematics and Computer Science
• Subjects: discrete t–s fuzzy hyperbolic model; parallel distributed compensation (pdc); positive diagonally dominant (pdd) matrices; robust stability
• Online Access: https://doi.org/10.1515/amcs-2016-0009

This paper focuses on the problem of constraint control for a class of discrete-time nonlinear systems. Firstly, a new discrete T–S fuzzy hyperbolic model is proposed to represent a class of discrete-time nonlinear systems. By means of the parallel distributed compensation (PDC) method, a novel asymptotic stabilizing control law with the “soft” constraint property is designed. The main advantage is that the proposed control method may achieve a small control amplitude. Secondly, for an uncertain discrete T–S fuzzy hyperbolic system with external disturbances, by the proposed control method, the robust stability and H∞ performance are developed by using a Lyapunov function, and some sufficient conditions are established through seeking feasible solutions of some linear matrix inequalities (LMIs) to obtain several positive diagonally dominant (PDD) matrices. Finally, the validity and feasibility of the proposed schemes are demonstrated by a numerical example and a Van de Vusse one, and some comparisons of the discrete T–S fuzzy hyperbolic model with the discrete T–S fuzzy linear one are also given to illustrate the advantage of our approach.