H_2/H_∞ Control for Stochastic Jump-Diffusion Systems with Markovian Switching

【摘要】：In this paper, a stochastic H_2/H_∞ control problem is investigated for Poisson jumpdiffusion 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_∞ control in terms of two sets of interconnected systems of Riccati type differential equations.