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Robust ℓ₁-Controller Design for Discrete-Time Positive T–S Fuzzy Systems Using Dual Approach

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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… Click to show full 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.

Keywords: controller design; discrete time; controller; design; time positive; inline formula

Journal Title: IEEE Transactions on Systems, Man, and Cybernetics: Systems
Year Published: 2022

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