On Stability and LQ Control of MJLS With a Markov Chain With General State Space

Author

Kordonis, Ioannis ; Papavassilopoulos, George P.

Author_Institution

Sch. of Electr. & Comput. Eng., Nat. Tech. Univ. of Athens, Athens, Greece

Volume

59

Issue

2

fYear

2014

fDate

Feb. 2014

Firstpage

535

Lastpage

540

Abstract

We study the mean square stability and the LQ control of discrete time Markov Jump Linear Systems where the Markov chain has a general state space. The mean square stability is characterized by the spectral radius of an operator describing the evolution of the second moment of the state vector. Two equivalent tests for the mean square stability are obtained based on the existence of a positive definite solution to a Lyapunov equation and a uniformity result respectively. An algorithm for testing the mean square stability is also developed based on the uniformity result. The finite and infinite horizon LQ problems are considered and their solutions are characterized by appropriate Riccati integral equations. An application to Networked Control Systems (NCS) is finally presented and a simple example is studied via simulation.

Keywords

Lyapunov methods; Markov processes; Riccati equations; discrete time systems; integral equations; linear quadratic control; linear systems; networked control systems; stability; state-space methods; LQ control; Lyapunov equation; Markov chain; NCS; Riccati integral equations; discrete time Markov jump linear systems; finite horizon LQ problems; infinite horizon LQ problems; mean square stability testing; networked control systems; simulation; spectral radius; state vector; Aerospace electronics; Delays; Equations; Markov processes; Mathematical model; Stability criteria; Markov jump linear systems; stochastic optimal control; stochastic stability;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2013.2274688

Filename

6567889