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.

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PDF(381 KB)
Journal of Systems Science & Complexity ›› 2021, Vol. 34 ›› Issue (3) : 924-954. DOI: 10.1007/s11424-020-9131-y

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

  • WANG Meijiao · MENG Qingxin · SHEN Yang
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Abstract

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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WANG Meijiao · MENG Qingxin · SHEN Yang. H2/H∞ Control for Stochastic Jump-Diffusion Systems with Markovian Switching. Journal of Systems Science and Complexity, 2021, 34(3): 924-954 https://doi.org/10.1007/s11424-020-9131-y
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