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

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