Switching fuzzy controller design based on switching Lyapunov function for a class of nonlinear systems

Abstract

This paper presents a switching fuzzy controller design for a class of nonlinear systems. A switching fuzzy model is employed to represent the dynamics of a nonlinear system. In our previous papers, we proposed the switching fuzzy model and a switching Lyapunov function and derived stability conditions for open-loop systems. In this paper, we design a switching fuzzy controller. We firstly show that switching fuzzy controller design conditions based on the switching Lyapunov function are given in terms of bilinear matrix inequalities, which is difficult to design the controller numerically. Then, we propose a new controller design approach utilizing an augmented system. By introducing the augmented system which consists of the switching fuzzy model and a stable linear system, the controller design conditions based on the switching Lyapunov function are given in terms of linear matrix inequalities (LMIs). Therefore, we can effectively design the switching fuzzy controller via LMI-based approach. A design example illustrates the utility of this approach. Moreover, we show that the approach proposed in this paper is available in the research area of piecewise linear control.

H∞ control design for discrete-time switched fuzzy systems

“…To obtain less conservative stability analysis results, [14] proposed switching fuzzy controller designs for a class of nonlinear systems, the stability conditions are obtained based on the switching Lyapunov function; [15] investigated a switching fuzzy controller design for a class of fuzzy T-S systems via a switching fuzzy model and a piecewise Lyapunov function, and new stability conditions are developed. Meanwhile, some relaxed stability conditions are proposed for continuous-time or discrete-time fuzzy T-S systems via piecewise Lyapunov functions in [16][17][18][19][20].…”

Output feedback robust stabilization of switched fuzzy systems with time-delay and actuator saturation

“…Based on the T-S fuzzy models (fuzzy systems), many significant control design methods and stability conditions have been obtained, for example, see [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Basic stability conditions [3][4][5][6] in terms of LMIs were obtained by using the Lyapunov functions theory.…”

“…Thus the obtained stability conditions are conservative. To obtain less conservative stability conditions, Ohtake et al [10,11] and Li et al [12,13] proposed switching fuzzy controller designs for a class of for a class of fuzzy systems, and the obtained stability conditions are based on the switching Lyapunov function; Wu et al [14] proposed the problems of stability analysis for a class of discrete-time T-S fuzzy systems with time-varying state delay based on a novel fuzzy LyapunovKrasovskii function; Yang and Dong [15], Wang et al [16], Dong and Yang [17,18] and Lam [19] investigated a switching fuzzy controller design for a class of fuzzy systems via a switching fuzzy model and a piecewise Lyapunov function, and new stability conditions were developed. However, the aforementioned controller design and stability analysis theories are only for the simple fuzzy systems, instead of switched fuzzy systems.…”

Stability and convergence analysis for a class of nonlinear passive systems

“…Particularly, this storage function is constructed as a switching storage function by using as generic function the original storage function easily obtained from the system passivity analysis. The approach of switching storage functions is based on a new efficient idea that has been developed to construct Lyapunov functions for difficult nonlinear systems [10,11] or hybrid systems [12]. Indeed, this approach effectively overcomes a fundamental problem in nonlinear stability analysis that is the construction of suitable storage functions.…”