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

Authors:
Weihai Zhang;Yulin Huang;Lihua Xie
Affiliations:
College of Information and Electrical Engineering, Shandong University of Science and Technology, Qingdao 266510, China;School of Electronic Information and Control Engineering, Shandong Institute of Light Industry, Jinan 250353, China;School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore
Venue:
Automatica (Journal of IFAC)
Year:
2008

Citing 6
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Brief paper: Stochastic H2/H∞ control for discrete-time systems with state and disturbance dependent noise

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Abstract

This paper studies the infinite horizon mixed H"2/H"~ control for discrete-time stochastic systems with state and disturbance dependent noise. We shall first establish a version of stochastic bounded real lemma (SBRL) which by itself has theoretical importance. Based on the SBRL, it is shown that under the condition of exact observability, the existence of a static state feedback H"2/H"~ controller is equivalent to the solvability of four coupled matrix-valued equations. A suboptimal H"2/H"~ controller design is given based on a convex optimization approach and an iterative algorithm is proposed to solve the four coupled matrix-valued equations.