Infinite horizon H2/H∞ control for discrete-time time-varying Markov jump systems with multiplicative noise

Authors:
Hongji Ma;Weihai Zhang;Ting Hou
Affiliations:
The Seventh Research Division, Beijing University of Aeronautics and Astronautics, Beijing, CO 100191, China and College of Information and Electrical Engineering, Shandong University of Science a ...;College of Information and Electrical Engineering, Shandong University of Science and Technology, Qingdao, CO 266510, China;College of Information and Electrical Engineering, Shandong University of Science and Technology, Qingdao, CO 266510, China
Venue:
Automatica (Journal of IFAC)
Year:
2012

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Abstract

In this paper we consider the infinite horizon H"2/H"~ control problem for discrete-time time-varying linear systems subject to Markov jump parameters and state-multiplicative noise. A stochastic version of a bounded real lemma is firstly developed for a general class of discrete-time time-varying Markov jump systems with state- and disturbance-multiplicative noise. By which we present a necessary and sufficient condition for the solvability of the H"2/H"~ control problem in terms of four coupled discrete-time Riccati equations. Moreover, the obtained design is applied to a macroeconomic problem to verify its effectiveness.