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H-control and the separation principle for discrete-time jump systems with the Markov chain in a general state space

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  • Danilo Zucolli Figueiredo
  • Oswaldo Luiz do Valle Costa

Abstract

This paper deals with the H2 optimal control problem of discrete-time Markov jump linear systems (MJLS) considering the case in which the Markov chain takes values in a general Borel space S$\mathcal {S}$. It is assumed that the controller has access only to an output variable and to the jump parameter. The goal, in this case, is to design a dynamic Markov jump controller such that the H2-norm of the closed-loop system is minimised. It is shown that the H2-norm can be written as the sum of two H2-norms, such that one of them does not depend on the control, and the other one is obtained from the optimal filter for an infinite-horizon filtering problem. This result can be seen as a separation principle for MJLS with Markov chain in a Borel space S$\mathcal {S}$ considering the infinite time horizon case.

Suggested Citation

  • Danilo Zucolli Figueiredo & Oswaldo Luiz do Valle Costa, 2017. "H-control and the separation principle for discrete-time jump systems with the Markov chain in a general state space," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(13), pages 2728-2741, October.
    • Handle: RePEc:taf:tsysxx:v:48:y:2017:i:13:p:2728-2741
    DOI: 10.1080/00207721.2017.1344331
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    1. Qiang Ling & Jing Li & Haojiang Deng, 2012. "Robust Speed Tracking of Networked PMSM Servo Systems with Uncertain Feedback Delay and Load Torque Disturbance," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-17, June.
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