Dissipative control of non-linear stochastic systems with Poisson jumps and Markovian switchings

This study discusses the dissipative control problem for a class of non-linear stochastic systems, which is driven by Brownian motion, Poisson random measure and Markovian process. By developing the dissipation theory for this class of systems, the equivalent conditions are established among the coupled Hamilton-Jacobi inequalities (HJIs), Hamilton-Jacobi equalities, the dissipative inequality and L₂-gain property. Then, a sufficient condition for the dissipative control of this class of systems is given in terms of N-coupled HJIs.