Control Synthesis of Fuzzy Semi-Markov Jump Systems With Incomplete Transition Information: A Homogeneous Polynomial-Based Approach

In this article, we concentrate on the stability and stabilization issues for the discrete-time Takagi-Sugeno (T-S) fuzzy semi-Markov jump systems (FS-MJSs) with incomplete transition probabilities (TPs). Since the statistical properties of mode transitions are frequently hard to get in practice, the system is built on the assumption that the information of TPs is partly accessed. Then, by making use of the incompletely discrete-time semi-Markov kernel, we offer the sufficient requisites for FS-MJSs mean square stability (MSS). We emphasize the impact of TPs on FS-MJSs by utilizing known TPs and introducing them into sufficient conditions for MSS. Numerically testable stability criteria for FS-MJSs in the sense of MSS are provided. The existence criteria are suggested to design the controller to guarantee the MSS of the closed-loop FS-MJSs. At the same time, a homogeneous polynomial technique is developed to reduce conservatism. The numerical examples demonstrate the effectiveness of our method.