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Infinite horizon $$H_2/H_\infty $$ optimal control for discrete-time Markov jump systems with ( $$x,u,v$$ )-dependent noise

Author

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  • Ting Hou
  • Weihai Zhang
  • Hongji Ma

Abstract

In this paper, an infinite horizon $$H_2/H_\infty $$ control problem is addressed for a broad class of discrete-time Markov jump systems with ( $$x,u,v$$ )-dependent noises. First of all, under the condition of exact detectability, the stochastic Popov–Belevich–Hautus (PBH) criterion is utilized to establish an extended Lyapunov theorem for a generalized Lyapunov equation. Further, a necessary and sufficient condition is presented for the existence of state-feedback $$H_2/H_\infty $$ optimal controller on the basis of two coupled matrix Riccati equations, which may be solved by a backward iterative algorithm. A numerical example with simulations is supplied to illustrate the proposed theoretical results. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Ting Hou & Weihai Zhang & Hongji Ma, 2013. "Infinite horizon $$H_2/H_\infty $$ optimal control for discrete-time Markov jump systems with ( $$x,u,v$$ )-dependent noise," Journal of Global Optimization, Springer, vol. 57(4), pages 1245-1262, December.
    • Handle: RePEc:spr:jglopt:v:57:y:2013:i:4:p:1245-1262
    DOI: 10.1007/s10898-012-0027-9
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