Stability and Control of Fuzzy Semi-Markov Jump Systems Under Unknown Semi-Markov Kernel

Abstract

This article investigates the stochastic stability analysis and stabilization problems for discrete-time Takagi–Sugeno fuzzy semi-Markov jump systems with upper-bounded sojourn time. The fuzzy rules can be different for different system modes. Consequently, the membership functions for fuzzy rules are dependent on the system modes. Allowing for the fact that semi-Markov kernel (SMK) are difficult to fully obtain in practice, the elements in the SMK of the underlying systems are deemed to be partly known, which is more general than both semi-Markov jump systems with completely available SMK and Markov jump systems with unknown transition probabilities. Afterward, the stability and stabilization conditions are established by part of the known SMK information and then by all the known SMK information. In the end, the validity and the superiority of our proposed theoretical results are exemplified via a single-link robot arm and a truck-trailer model.