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

Ting Hou (), Weihai Zhang () and Hongji Ma ()

Journal of Global Optimization, 2013, vol. 57, issue 4, 1245-1262

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

Keywords: Infinite horizon; $$H_2/H_\infty $$ control; Markov jump; Exact detectability; Coupled matrix Riccati equations (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10898-012-0027-9

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