LQ Control of Discrete-Time Jump Systems With Markov Chain in a General Borel Space

Author(s)

Costa, O. L. V. ^[1] ; Figueiredo, D. Z. ^[1]

Affiliation

^[1] Univ Sao Paulo, Dept Engn Telecomunicacoes & Controle, Escola Politecn, Sao Paulo - Brazil

• Document type: Journal article
• Source: IEEE Transactions on Automatic Control; v. 60, n. 9, p. 2530-2535, SEP 2015.
• Web of Science Citations: 6

Abstract

In this technical note, it is studied the LQ-optimal control problem for discrete-time Markov jump linear systems considering the case in which the Markov chain takes values in a general Borel space M. It is shown that the solution of the LQ-optimal control problem is obtained in terms of the positive semi- definite solution S(l), l epsilon M, of M-coupled algebraic Riccati equations. By M-coupled we mean that the algebraic Riccati equations are coupled via an integral over a transition probability kernel G(.|.) having a density g(.|.) with respect to a sigma-finite measure mu on M. It is obtained sufficient conditions, based on the concept of stochastic stabilizability and stochastic detectability, for the existence and uniqueness of this positive semi-definite solution. These results generalize previous ones in the literature, which considered only the case of the Markov chain taking values in a finite or infinite countable space. (AU)