An SOS-Based Sliding Mode Controller Design for a Class of Polynomial Fuzzy Systems

This paper investigates the problem of designing a robust controller for continuous polynomial fuzzy systems with external disturbances. The input matrix B-i (x) of the considered system is not equal to one another. To solve this problem, first, we rewrite every column vector of input matrix B-i(x) using the vectors of the basis matrix B(x). Second, by use of the column vector of B(x), the subsliding mode surface s(p) (t) is designed. Based on the rewritten system, a novel sliding mode surface s(t) is devised. The sliding mode surface parameter matrix can be characterized in terms of the solution of the provided sum of squares conditions. Then, a sliding mode controller is proposed to stabilize the considered system. It could make the state of the considered system drive onto s(t) and avoid the state escaping from the surface in the subsequent time. A lemma is provided to obtain the final result. Finally, practical and numerical examples are provided to demonstrate the validity of the proposed approach.