Inverse optimal gain assignment control for Markovian jump nonlinear systems

The concept of input-to-state stability in probability is introduced and an input-to-state stabilization protocol is proposed for a class of strict feedback Markovian jump nonlinear systems. It is shown that the existence of a group of input-to-state stable control Lyapunov function with small control is a sufficient condition for the solvability of the inverse optimal gain assignment problem. Finally using backstepping method we construct a smooth feedback control law for a class of strict feedback nonlinear systems. To deal with the coupling item caused by Markovian jump the Lyapunov function and the controller are designed independently of the operation mode.