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

WANG Meijiao · MENG Qingxin · SHEN Yang   

  1. WANG Meijiao
    Business School, University of Shanghai for Science and Technology, Shanghai 200093, China.
    Email: mjiao wang@163.com.
    MENG Qingxin (Corresponding author)
    Department of Mathematical Sciences, Huzhou University, Zhejiang 313000, China. Email: mqx@zjhu.edu.cn.
    SHEN Yang
    School of Risk & Actuarial Studies, University of New South Wales, Sydney, NSW 2052, Australia.
    Email: skyshen87@gmail.com.
  • Online:2021-06-25 Published:2021-03-11

WANG Meijiao · MENG Qingxin · SHEN Yang. H2/H∞ Control for Stochastic Jump-Diffusion Systems with Markovian Switching[J]. Journal of Systems Science and Complexity, 2021, 34(3): 924-954.

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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