H 2 optimal control for a wide class of discrete-time linear stochastic systems

• Published in: International journal of systems science Vol. 40; no. 10; pp. 1029 - 1049
• Main Authors: Dragan, Vasile, Morozan, Toader
• Format: Journal Article
• Language: English
• Published: Taylor & Francis Group 01.10.2009
• Subjects: discrete-time linear systems; independent random perturbations; Markov chains; Markov processes; norms; optimal control; Primary: 93E20; robust control; Secondary: 93C55; stochastic systems
• ISSN: 0020-7721; 1464-5319
• DOI: 10.1080/00207720902974629

In this article, the problem of H 2 -control of a discrete-time linear system subject to Markovian jumping and independent random perturbations is considered. Different H 2 performance criteria (often called H 2 -norms) are introduced and characterised via solutions of some suitable linear equations on certain spaces of symmetric matrices. Some aspects specific to the discrete-time framework are revealed. The problem of optimisation of H 2 -norms is solved under the assumption that full state vector is available for measurements. One shows that among all stabilising controllers of higher dimension, the best performance is achieved by a zero-order controller. The corresponding feedback gain of the optimal controller is constructed based on the stabilising solution of a system of discrete-time generalised Riccati equations.