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 $\mathbf {B}_i(x)$ of the considered system is not equal to one another. To solve this problem, first, we rewrite every column vector of input matrix $\mathbf {B}_i(x)$ using the vectors of the basis matrix $\mathbb {B}(x)$. Second, by use of the column vector of $\mathbb {B}(x)$ , 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. [ABSTRACT FROM AUTHOR]