Reachable Set Estimation for Ito Stochastic Semi-Markovian Jump Systems Against Multiple Time Delays

The work deals with these issues of stochastic finite-time boundedness (SFTB), reachable set estimation with input-output finite-time mean square stabilization (IO-FTMSS) for multiple state delayed semi-Markovian jump models subject to uncertainties, stochastic process as well as input constraint. There are few attempts to perform related studies. Firstly, a nonlinear passive control mechanism is designed. Then, a closed-loop model could be acquired. Through stochastic Lyapunov function, these problems of SFTB, reachable set estimation with IO-FTMSS could be solved. In addition, these stability conditions are provided in the framework of linear matrix inequalities. These controller gain matrices, meanwhile, can be derived. At last, this availability of this described strategy can be proved through one simulation.

Automated summary

This work focuses on studying the problems of stochastic finite-time boundedness (SFTB) and reachable set estimation with input-output finite-time mean square stabilization (IO-FTMSS) for multiple state delayed semi-Markovian jump models subject to uncertainties, stochastic process as well as input constraint. A nonlinear passive control mechanism is designed and utilized to achieve a closed-loop model. The problems of SFTB and IO-FTMSS are then solved through the stochastic Lyapunov function. The stability conditions are provided using linear matrix inequalities and the controller gain matrices can be derived. The feasibility of the proposed strategy is demonstrated through simulation.