Stability and Stabilization Analysis of Interval Positive Takagi-Sugeno Fuzzy Systems by using Convex Optimization

TL;DR

This paper presents a convex optimization-based method for analyzing and designing stabilizing controllers for positive Takagi-Sugeno fuzzy systems, ensuring stability and positivity through linear programming.

Contribution

It introduces a new approach using co-positive Lyapunov functions and convex optimization for stability analysis and controller design of positive fuzzy systems.

Findings

The method guarantees stability and positivity of the closed-loop system.

Optimal controllers are obtained via linear programming.

Numerical examples demonstrate the effectiveness of the approach.

Abstract

In this paper, the stability and stabilization problem of positive nonlinear systems, described by the Takagi-Sugeno discrete-time fuzzy model, is studied. The proposed approach is based on the linear co-positive Lyapunov function and parallel distributed controller. Necessary and sufficient conditions for the existence of a state feedback controller, which guarantees the positivity and stability of the closed-loop system, are obtained by a new approach as linear programming, and to solve it and obtain the controller coefficients, the optimal Convex Optimization algorithm is used. Moreover, the design of the robust controller has been considered. Finally, a numerical and practical example is presented to illustrate the validity and effectiveness of the designed method. Keywords: Linear Programming, Co-positive Linear Lyapunov function, Takagi-Sugeno Fuzzy Systems, Positive Systems.