Finite-time H∞ control for extended Markovian jump systems with partially known transition probabilities

This note addresses the problem of finite-time H_∞ control for a class of extended Markovian jump systems. The stochastic process of given system is described by a Markovian chain, and the knowledge of transition jump rates is inaccurate. In this case, the theoretical results on finite-time boundedness, H_∞ finite-time boundedness and finite-time H_∞ state feedback stabilization, are developed, respectively. Then, the purpose is to design a finite-time H_∞ state feedback controller so that the corresponding closed-loop system result to be finite-time boundedness. It is shown that the corresponding existence conditions are presented via a set of strict linear matrix inequalities. Finally, a numerical example is given to demonstrate the effectiveness of the proposed theoretical results.