Almost Sure Finite-Time Control for Markovian Jump Systems Under Asynchronous Switching With Applications: A Sliding Mode Approach

The almost sure finite-time sliding mode control issue is investigated for Markov jump systems. The switching asynchronism between the constructed controller and considered systems is studied. The influence of time-varying delays and disturbances on systems is fully considered, and the sliding mode controller design within a finite time interval is extended to the probability framework. First, the finite time interval is divided into the reaching and the sliding motion phases, and the almost sure finite-time boundedness is analyzed in both phases. Second, the sliding mode controller gain is determined by the provided linear matrix inequality-based criteria. Finally, a numerical example and DC-DC buck converter circuit example verify the effectiveness and less conservativeness of our method.