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

• Published in: Automatica (Oxford) Vol. 48; no. 7; pp. 1447 - 1454
• Main Authors: Ma, Hongji, Zhang, Weihai, Hou, Ting
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.07.2012; Elsevier
• Subjects: [formula omitted] control; Applied sciences; Computer science; control theory; systems; Control system analysis; Control theory. Systems; Discrete-time systems; Exact sciences and technology; Markov parameters; Multiplicative noise; Riccati equations; Time-varying systems; Discrete-time systems; H2/H∞ control; Multiplicative noise; Markov parameters; Riccati equations; Time-varying systems; Markov process; Bounded real lemma; Probabilistic approach; H2 control; Necessary and sufficient condition; H infinite control; H; control; Hybrid system; Time varying system; optimization; Discrete time; Jump process; Infinite horizon; Macroeconomics; Riccati equation; Solvability
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2012.05.006

In this paper we consider the infinite horizon H2/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 H2/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.