Observer design of discrete time T-S fuzzy systems with measurable premise variables based on common quadratic Lyapunov function

This article studies the problem of global stability of the Takagi–Sugeno fuzzy systems based on a novel descriptor-based non-quadratic Lyapunov function. A modified non-quadratic Lyapunov function, which comprises an integral term of the membership functions, and a modified non-parallel distributed controller constructed by constant delayed premise variables are considered that assure the global stability of the closed-loop T–S fuzzy system. The special structure of the used non-quadratic Lyapunov function results in time-delayed terms of the membership functions, instead of appearing their time derivatives, which is the well-known issue of the common non-quadratic Lyapunov functions in the literature. Also, the memory fuzzy controller is chosen such that the artificial constant delay-dependent stability analysis conditions for a non-delayed closed-loop T–S fuzzy system are formulated in terms of linear matrix inequalities. To further reduce the conservatives, some slack matrices are introduced by deploying the descriptor representation and decoupling lemmas. Moreover, the design of the robust fuzzy controller is studied through the [Formula: see text] performance criteria. The main advantages of the proposed approach are its small conservatives and the global stability analysis, which distinguish it from the state-of-the-art methods. To show the merits of the proposed approach, comparison results are provided, and two numerical case studies, namely, flexible joint robot and two-link joint robot are considered.

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Observer design of discrete-time T–S fuzzy systems via multi-instant augmented multi-indexed matrix approach

Journal of the Franklin Institute ◽

10.1016/j.jfranklin.2015.05.023 ◽

2015 ◽

Vol 352 (7) ◽

pp. 2899-2919 ◽

Cited By ~ 21

Author(s):

Xiang-Peng Xie ◽

Dong Yue ◽

Chen Peng

Keyword(s):

Discrete Time ◽

Fuzzy Systems ◽

Observer Design ◽

Matrix Approach

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Stabilization of a certain class of fuzzy control systems with uncertainties

Archives of Control Sciences ◽

10.1515/acsc-2017-0028 ◽

2017 ◽

Vol 27 (3) ◽

pp. 453-481

Author(s):

Nizar Hadj Taieb ◽

Mohamed Ali Hammami ◽

François Delmotte

Keyword(s):

Lyapunov Function ◽

Exponential Stability ◽

Control Systems ◽

Fuzzy Systems ◽

Closed Loop ◽

Exponential Convergence ◽

Closed Loop System ◽

Quadratic Lyapunov Function ◽

Integrable Functions ◽

Takagi Sugeno

AbstractIn this paper, we investigate the global uniform practical exponential stability for a class of uncertain Takagi-Sugeno fuzzy systems. The uncertainties are supposed uniformly to be bounded by some known integrable functions to obtain an exponential convergence toward a neighborhood of the origin. Therefore, we use common quadratic Lyapunov function (CQLF) and parallel distributed compensation (PDC) controller techniques to show the global uniform practical exponential stability of the closed-loop system. Numeric simulations are given to validate the proposed approach.

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