Composite Disturbance-observer-based Control and MPC for Discrete-Time T-S Fuzzy Semi-Markovian Jump Systems

This technical note discusses the stability and stabilization problems for Takagi-Sugeno (T-S) fuzzy semi-Markovian jump systems (S-MJSs) in the discrete-time domain subjected to matched disturbances. The disturbance observer is designed to estimate the external disturbance. And then by combining the disturbance observer with model predictive control (MPC), a composite controller is proposed, such that, the stability of the closed-loop system can be guaranteed. By constructing a proper sojourn-time-dependent Lyapunov function, in the form of linear matrix inequalities (LMI), sufficient conditions for the existence of the composite anti-disturbance controller are framed. Finally, a set of numerical simulation examples are used to prove the effectiveness and feasibility of the proposed control strategy.