Fuzzy Control System Design via Fuzzy Lyapunov Functions

Abstract

This correspondence deals with the problems of analysis and design for a class of continuous-time Takagi-Sugeno fuzzy control systems. Sufficient conditions for the stability of fuzzy control systems are derived based on a fuzzy Lyapunov function. Both parallel and nonparallel distributed compensation controllers are considered. Sufficient conditions for the solvability of the controller design problem are given in the form of linear matrix inequalities. Unlike the fuzzy Lyapunov function approaches reported in the literature, the bound of the time derivatives of the fuzzy basis functions is not required in the proposed approaches. The effectiveness of the proposed approaches is shown through a numerical example.

Fuzzy Diffusion Distance Learning for Cartoon Similarity Estimation

“…However, such exactness is not always possible. The fuzzy set theory proposed in [25][26] is a precise mathematical tool for processing data derived from vague sources.…”

“…Compute the eigenvectors and eigenvalues for the Markov matrix and get the diffusion coordinates for the data in the original space shown in (26). The cartoon similarity is evaluated by calculating the distance in the low-dimensional space.…”

PDC and Non-PDC fuzzy control with relaxed stability conditions for contintuous-time multiplicative noised fuzzy systems

“…Using the nonquadratic Lyapunov function, some scholars have derived the relaxed stability conditions for the discrete-time [19][20][21] and continuous-time [22][23][24][25][26][27][28][29][30][31] T-S fuzzy systems. However, the multiplicative noise was not considered for the systems in [19][20][21][22][23][24][25][26][27][28][29][30][31]. Considering the stochastic behaviors, a Non-PDC fuzzy control scheme is thus developed in this paper by using the nonquadratic Lyapunov function for the T-S fuzzy systems with multiplicative noises.…”

Relaxed stabilization conditions for continuous-time Takagi–Sugeno fuzzy control systems

“…The problem of stabilization for T-S fuzzy control systems has been paid much attention [2][3][4]6,7,[9][10][11][12][13][14][15][16][17][19][20][21]. The common Lyapunov function and PDC control law were proposed in [4,6,7,11,14,17,19,21] to design controllers which can stabilize the systems.…”

“…Recently, [16] constructed a new fuzzy Lyapunov function for a class of T-S fuzzy systems, and such fuzzy Lyapunov function eliminated the requirement on the time-derivative information of the membership functions. Based on the new function, further relaxed stabilization conditions were obtained in [13,15]. However, the time-derivative information can only be eliminated under a particular premise structure of the T-S fuzzy model.…”