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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Stabilizability and positiveness of solutions of the jump linear quadratic problem and the coupled algebraic Riccati equation

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Author(s):
Costa, E. F. ; Val, João Bosco Ribeiro do [2]
Total Authors: 2
Document type: Journal article
Source: IEEE Transactions on Automatic Control; v. 50, n. 5, p. 691-695, 2005.
Field of knowledge: Engineering - Electrical Engineering
Abstract

This note addresses the jump linear quadratic problem of Markov jump linear systems and the associated algebraic Riccati equation. Necessary and sufficient conditions for stability of the optimal control and positiveness of Riccati solutions are developed. We show that the concept of weak detectability is not only a sufficient condition for the finiteness of cost functional to imply stability of the associated trajectory, but also a necessary one. This, together with a characterization developed here for the kernel of the Riccati solution, allows us to show that the control solution stabilizes the system if and only if the system is weakly detectable, and that the Riccati solution is positive-definite if and only if the system is weakly observable. The connection between the algebraic Riccati equation and the control problem is made, as far as the minimal positive-semidefinite solution for the algebraic Riccati equation is identified with the optimal solution of the linear quadratic problem. Illustrative numerical examples and comparisons are included. (AU)

FAPESP's process: 03/06736-7 - Control and filtering of Markovian jumping parameters stochastic systems
Grantee:João Bosco Ribeiro do Val
Support type: Research Projects - Thematic Grants