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

Authors:
Ting Hou;Weihai Zhang;Hongji Ma
Affiliations:
College of Science, Shandong University of Science and Technology, Qingdao, China 266590;College of Information and Electrical Engineering, Shandong University of Science and Technology, Qingdao, China 266590;College of Science, Shandong University of Science and Technology, Qingdao, China 266590
Venue:
Journal of Global Optimization
Year:
2013

Citing 5
Cited 0

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Indefinite Stochastic Linear Quadratic Control with Markovian Jumps in Infinite Time Horizon

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State Feedback $H_\infty$ Control for a Class of Nonlinear Stochastic Systems

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Infinite horizon stochastic H2/H∞ control for discrete-time systems with state and disturbance dependent noise

Automatica (Journal of IFAC)
Brief paper: A unified design for state and output feedback H∞ control of nonlinear stochastic Markovian jump systems with state and disturbance-dependent noise

Automatica (Journal of IFAC)

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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.