Affiliations: [a] School of Mathematics and Statistics, Xidian University, Xi’an, China
| [b]
Xi’an Institute of Optics and Precision Mechanics of CAS, Xi’an, China
Correspondence:
[*]
Corresponding author. Junmin Li, School of Mathematics and Statistics, Xidian University, Xi’an 710071, China. E-mail: jmli@mail.xidian.edu.cn.
Abstract: In this paper, a Takagi-Sugeno (T-S) fuzzy hyperbolic model is proposed for the fuzzy control of a class of nonlinear systems. The consequence of the proposed model is a hyperbolic tangent dynamic model, and it is employed to represent the nonlinear system. By constructing a new Lyapunov function, the stability conditions of the open-loop T-S fuzzy hyperbolic system are derived via linear matrix inequalities (LMIs). Then, the parallel distributed compensation (PDC) method is used to design a fuzzy hyperbolic controller, and the asymptotic stability conditions of the closed-loop system are formulated via LMIs. The main advantage of the control based on T-S fuzzy hyperbolic model is that it can achieve small control amplitude via “soft” constraint control approach. Finally, the effectiveness and advantage of the proposed schemes are illustrated by a mathematical constructive example and the Van de Vusse example.
Keywords: Nonlinear systems, T-S fuzzy hyperbolic model, small control amplitude, fuzzy control, linear matrix inequalities (LMIs)
