H2/H∞ Control for Stochastic Jump-Diffusion Systems with Markovian Switching

In this paper, a stochastic H-2/H-infinity control problem is investigated for Poisson jump-diffusion systems with Markovian switching, which are driven by a Brownian motion and a Poisson random measure with the system parameters modulated by a continuous-time finite-state Markov chain. A stochastic jump bounded real lemma is proved, which reveals that the norm of the perturbation operator below a given threshold is equivalent to the existence of a global solution to a parameterized system of Riccati type differential equations. This result enables the authors to obtain sufficient and necessary conditions for the existence of H-2/H-infinity control in terms of two sets of interconnected systems of Riccati type differential equations.