Further Results on Robust Output-Feedback Dissipative Control of Markovian Jump Fuzzy Systems with Model Uncertainties

This paper investigates an improved criterion to synthesize dissipative observer-based controllers for Markovian jump fuzzy systems under model uncertainties. Since fuzzy-basis functions include some immeasurable state variable or uncertain parameters, there are differences in the fuzzy-basis functions between controller and plant, which is a mismatched phenomenon. This work presents the first attempt for applying double-fuzzy summation-based Lyapunov functions for the observer-based control scheme of the Markov jump fuzzy system regarding the mismatched phenomenon. To be specific, the dissipative conditions are formulated in terms of uncertain parameterized bilinear matrix inequalities. Based on the improved relaxation techniques, a linear-matrix-inequality (LMI)-based algorithm is proposed in the framework of sequence linear programming matrix method. The obtained observer-based controller ensures that the closed-loop system is stochastically stable, and the dissipative performances produce less conservative results compared to preceding works via two numerical examples.