Robust ℓ-Controller Design for Discrete-Time Positive T-S Fuzzy Systems Using Dual Approach

Document Type

Article

Publication Date

2-1-2022

Publication Title

IEEE Transactions on Systems, Man, and Cybernetics: Systems

Volume

52

Issue

2

First Page

706

Keywords

Linear co-positive Lyapunov function (LCPLF), linear programming (LP) framework, positive systems, Takagi-Sugeno (T-S) fuzzy systems

Last Page

715

Abstract

In this article, a new approach is proposed for stability analysis and controller design of nonlinear discrete-time positive systems by means of the Takagi-Sugeno fuzzy model. The closed-loop stability and the positivity constraint are guaranteed by synthesizing a linear co-positive Lyapunov function and by applying the parallel distributed compensation controller. In contrast to the state-of-the-art approaches for ensuring the ell {1} -stability of the positive system which are based on bilinear matrix inequalities, the proposed optimal robust control design under ell {1} -induced performance is derived based on linear programming framework. It has been shown that the computational complexity of the proposed optimization problem can be effectively reduced. Finally, a numerical example and the Leslie population model are adopted to show the capabilities of the proposed method.

DOI

10.1109/TSMC.2020.3013161

ISSN

21682216

E-ISSN

21682232

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