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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. [ABSTRACT FROM AUTHOR]

This paper is concerned with linear matrix inequality conditions to design observer-based H ∞ -controllers for discrete-time Markov jump fuzzy systems with regard to incomplete transition probabilities and sensor failures. Since some system states involved in fuzzy premise variables are immeasurable or under sensor failures, the observer-based fuzzy controller does not share the same fuzzy basic functions with plants, leading to a mismatch phenomenon. Our work contributes a new single-step LMI method for synthesizing the observer-based controller of the Markov jump fuzzy system in the presence of sensor failures with regard to the mismatched phenomenon. The non-convex H ∞ -stabilization conditions induced by the output-feedback scheme are firstly formulated in terms of multiple-parameterized linear matrix inequalities (PLMIs). Secondly, by assuming that the differences of fuzzy basic functions between the controller and plant are bounded, the multi-PLMI-based conditions are cast into linear matrix inequalities standing for tractable conditions. The designed observer-based controller guarantees the stochastic stability of the closed-loop system and less conservative results compared to existing works in three numerical examples. [ABSTRACT FROM AUTHOR]