Stochastic Finite-time Stability Study For Two Class Of Semi-Markovian Jump Systems

In recent years,the semi-Markovian jump system has been widely concerned in the field of control and engineering science.The so-called semi-Markovian jump system,that is,because of the influence and interference of various uncertain factors,in the process of system operation,the jump and dwell time of the system are random.Finitetime stability means that the state of the system does not exceed a certain threshold value in a limited time,and it can reflect the transient performance of the system.In order to reduce the consumption of time and resources during data transmission,we construct the event-triggered mechanism.In this paper,we study the stochastic finitetime stability and the stochastic finite-time boundedness of two class of systems under the assumption that the transition probabilities are general uncertain or completely known.And we analyze the extended dissipative performance of the system.Firstly,we construct Lyapunov function and Lyapunov functional,in terms of the solutions of linear matrix inequalities,the sufficient conditions of stochastic finite-time stability and stochastic finite-time boundedness are given.Secondly,the corresponding state feedback controllers are designed according to the obtained conditions,so that the system has the extended dissipative performance at the same time of stability.Finally,the effectiveness of the theoretical results is illustrated by simulation examples.