Average Cost and Stability of Time-Varying Linear Systems

Author

Vargas, Alessandro N. ; Val, João B R do

Author_Institution

Depto. de Telematica, Univ. Estadual de Campinas, Campinas, Brazil

Volume

55

Issue

3

fYear

2010

fDate

3/1/2010 12:00:00 AM

Firstpage

714

Lastpage

720

Abstract

In this technical note, the stability for time-varying discrete-time stochastic linear systems, with possibly unbounded trajectories, is associated to the existence of the long-run average cost criteria. Under controllability and observability, the stochastic system is stable in the sense that its state tends asymptotically to the origin in the mean. Further conditions related to a lower bound on the long-run average cost, or with periodic time-varying systems, provides uniform second moment stability.

Keywords

asymptotic stability; controllability; linear systems; observability; stochastic systems; controllability; discrete-time system; linear system; observability; second moment stability; stability; stochastic system; time-varying system; unbounded trajectories; Additive noise; Controllability; Costs; Covariance matrix; Filtering; Linear systems; Nonlinear filters; Observability; Riccati equations; Signal processing; Stability; Stability criteria; State estimation; Stochastic systems; Time varying systems; Long run average cost; stability of time-varying systems; stochastic linear systems;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2010.2040423

Filename

5409508