Relaxed Observer-Based H ∞ -Control for Markov Jump Fuzzy Systems with Incomplete Transition Probabilities and Sensor Failures

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.