Input-output finite-time stability and stabilization of stochastic Markovian switching systems under finite-time boundedness

This paper investigates finite-time mean square boundedness (FTMSB) and input-output finite-time mean square stability (IO-FTMSS) of stochastic Markovian switching systems (SMSSs). Simultaneous consideration is given to the state and output stability to prevent the occurrence of huge and unacceptable values throughout certain transient periods. Utilizing a collection of linear matrix inequalities (LMIs), a sufficient condition for the system satisfying both FTMSB and IO-FTMSS is developed for a class of bounded input signals. Furthermore, via state feedback and output feedback, two controllers are developed to achieve the closed-loop system both FTMSB and IO-FTMSS. The proposed criteria ensure that the state and output of SMSSs remain within a designated threshold over the specified time interval. Finally, to illustrate the feasibility of the suggested technique, two examples are shown.