
H2/H∞ Control for Stochastic Jump-Diffusion Systems with Markovian Switching
WANG Meijiao · MENG Qingxin · SHEN Yang
Journal of Systems Science & Complexity ›› 2021, Vol. 34 ›› Issue (3) : 924-954.
H2/H∞ Control for Stochastic Jump-Diffusion Systems with Markovian Switching
In this paper, a stochastic H2/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 H2/H∞ control in terms of two sets of interconnected systems of Riccati type differential equations.
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