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

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Abstract

In this paper, a stochastic H2/H 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 H2/H control in terms of two sets of interconnected systems of Riccati type differential equations.

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Correspondence to Qingxin Meng.

Additional information

This work was supported by the National Natural Science Foundation of China under Grant No. 11871121 and the Natural Science Foundation of Zhejiang Province for Distinguished Young Scholar under Grant No. LR15A010001.

This paper was recommended for publication by Editor SUN Jian.

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Wang, M., Meng, Q. & Shen, Y. H2/H Control for Stochastic Jump-Diffusion Systems with Markovian Switching. J Syst Sci Complex 34, 924–954 (2021). https://doi.org/10.1007/s11424-020-9131-y

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  • DOI: https://doi.org/10.1007/s11424-020-9131-y

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