Stability Analysis of General Polynomial Fuzzy Model-Based Control Systems

Abstract

This chapter investigates the stability of general polynomial fuzzy model-based control systems. In most of the published results, a constraint that the polynomial Lyapunov function matrix is allowed to be dependent on some state variables determined by the structure of the input matrices is required to obtain convex stability conditions. In this chapter, this constraint is removed and a two-step procedure is proposed to search for a feasible solution to the SOS-based stability conditions. Consequently, the stability analysis results can be applied to a wider range of polynomial-fuzzy model-based control systems. Furthermore, three cases of polynomial fuzzy controllers under perfectly, partially and imperfectly matched premises are considered. Their levels of controller complexity, design flexibility and stability analysis results are discussed and compared. Simulations examples are given to compare among the three cases in terms of capability of find feasible solutions and show that the proposed analysis results outperform some published ones.