Finite-time H∞H∞ control for singular Markovian jump systems with partly unknown transition rates

This paper investigates the problem of finite-time H∞H∞ control for a class of singular Markovian jump systems with partly unknown transition rates. Firstly, sufficient conditions on singular stochastic finite-time boundedness of singular Markovian jump systems with partly unknown transition rates are obtained. Secondly, the results are extended to singular stochastic H∞H∞ finite-time boundedness of singular Markovian jump systems with partly unknown transition rates. Then state feedback controllers are designed to ensure the singular stochastic finite-time boundedness and the singular stochastic H∞H∞ finite-time boundedness of the underlying closed singular Markovian jump systems in the forms of strict LMIs. Finally, numerical examples are given to illustrate the validity of the proposed methods.