Finite-time dissipative control for stochastic interval systems with time-delay and Markovian switching

The finite-time stochastically boundedness (FTSB) and the finite-time strictly stochastically exponential dissipative (FTSSED) control problems for the stochastic interval systems, which are encountered the time-delay and Markovian switching, are investigated in this paper. The stochastic delayed interval systems with Markovian switching (SDISswMS) are equivalently transformed into a kind of stochastic uncertain time-delay systems with Markovian switching by interval matrix transformation. Some sufficient conditions of FTSB and FTSSED for the stochastic delayed interval systems with Markovian switching are obtained, and the FTSB and FTSSED controllers are designed by solving a series of linear matrix inequalities, which are solvable by LMIs toolbox. Finally, a numerical example with simulations is given to illustrate the correctness of the obtained results and the effectiveness of the designed controller.