Switching controller design for a class of Markovian jump nonlinear systems using stochastic small-gain theorem

Switching controller design for a class of Markovian jump nonlinear systems with unmodeled dynamics is considered in this paper. Based on the differential equation and infinitesimal generator of jump systems, the concept of Jump Input-to-State practical Stability (JISpS) in probability and stochastic Lyapunov stability criterion are put forward. By using back setpping technology and stochastic small-gain theorem, a switching controller is proposed which ensures JISpS in probability for the jump nonlinear system. A simulation example illustrates the validity of this design.