Stabilization of Nonlinear Systems Case

This chapter focuses on the issue of nonlinear semi-Markov singularly perturbed systems (SPSs) using a fuzzy model-based approach. This chapter uses semi-Markov Kernel (SMK) to calculate controller gains by using linear matrix inequality technology based on T-S fuzzy mode. In this chapter, the SMK is divided into two cases, the first section considers SMK with complete probability state information, and the second part includes the case of limited access to probabilistic information. The analytical criteria of \(\delta \) -error mean square stable ( \(\delta \) -MSS) is formulated, and corresponding controllers are designed for the two situations. Finally, the established theoretical results are further validated through numerical examples.