H control synthesis for short-time markovian jump continuous-time linear systems

In many actual engineering applications, the Markovian jump among subsystems often occurs in some short finite-time intervals. For this class of Markovian jump systems, called short-time Markovian jump systems in this paper, the state boundedness during the short-time Markovian jump interval is of great interest. By introducing the concepts of finite-time stochastic stability and boundedness, sufficient conditions ensuring short-time Markovian jump system to be H finite-time stochastic bounded are derived. Then, the control synthesis problem is studied, where both asymptotic stability and finite-time stochastic boundedness are considered. Finally, an LMI-based design algorithm is proposed to solve the control synthesis problem. Several numerical examples are given to illustrate the results proposed in this paper.