Observer-based finite-time stabilization for extended Markov jump systems

In this paper, we study the problem of observer-based finite-time stabilization\ud for a class of extended Markov jump systems with norm-bounded\ud uncertainties and external disturbances. The stochastic character under consideration\ud is governed by a finite-state Markov process, but with only partial\ud information on the transition jump rates. Based on the finite-time stability\ud analysis, sufficient conditions for the existence of the observer-based controller\ud are derived via a linear matrix inequality approach such that the closed-loop\ud system trajectory stays within a prescribed bound in a fixed time interval.\ud When these conditions are satisfied, the designed observer-based controller\ud gain matrices can be obtained by solving a convex optimization problem.\ud Simulation results demonstrate the effectiveness of the approaches proposed\ud in this paper