Finite horizon H2/H∞ control for nonlinear Markov jump systems

This paper describes the problem of finite horizon H
₂
/H
_∞
control for nonlinear stochastic Markov jump systems governed by Itô-type equations with state, control and external disturbance dependent noise. We firstly derived nonlinear stochastic bounded real lemma and nonlinear optimal regular problem for the considered system. Further, it was showed that the finite horizon H
₂
/H
_∞
control under consideration is associated with the four cross-coupled Hamilton-Jacobi equations. A sufficient condition and a necessary condition for the existence of the H
₂
/H
_∞
controller were presented respectively.