Improved Reachable Set Estimation and Aperiodic Sampled-Data for T–S Fuzzy Markovian Jump Systems

Abstract

In this article, the problem of reachable set estimation (RSE) and the design of aperiodic sampled-data controller for Takagi–Sugeno fuzzy Markovian jump systems (T–S FMJSs) with unit-energy bounded disturbance (UEBD) and unit-peak bounded disturbance (UPBD) inputs are taken into consideration. First, sufficient conditions that all states of the T–S FMJSs are encompassed by ellipsoids under zero initial conditions are acquired via constructing a mode-dependent two-sided loop-based Lyapunov function and applying a linear matrix inequality approach. Second, the RSE is taken into account in the design of the state feedback aperiodic sampled-data controller with the aim that the resulting ellipsoid encompasses the reachable set of the closed-loop system. Finally, a nonlinear mass-spring model and a tunnel diode circuit model demonstrate the efficiency of the presented approach. In addition, this method is able to obtain a larger sampled-data period than other literature, thus saving bandwidth and reducing communication resources.