Design and Analysis of Polynomial Positive Fuzzy System Controllers Based on Markov Transitions

This study explores polynomial Markov positive fuzzy systems, formulating controllers for these systems by examining the prerequisites for positivity and stochastic stability. Initially, polynomials are incorporated into the Markov positive fuzzy system to represent nonlinear elements better and enhance its capacity to model nonlinear systems. Concurrently, the study discusses the non-convex scenarios encountered in the stability analysis of the closed-loop system once the positive fuzzy system controller is integrated and confirms the stability of the Markov polynomial positive fuzzy system. Ultimately, the effectiveness of the proposed approaches is demonstrated through a numerical simulation example.