Cyclomonotonicity and stabilizability properties of solutions of the difference periodic Riccati equation

Author

De Nicolao, Giuseppe

Author_Institution

Dipartimento di Elettron., Politecnico di Milano, Italy

Volume

37

Issue

9

fYear

1992

fDate

9/1/1992 12:00:00 AM

Firstpage

1405

Lastpage

1410

Abstract

The Kalman filter associated with a discrete-time linear T-periodic system is tested. The problem considered is that of selecting an initial covariance matrix such that the periodic filter based on the first T values of the Kalman filter gain is stabilizing. Sufficient conditions are given that hinge on the cyclomonotonicity of the solution of the periodic Riccati equation. Potential applications are found in filter design, quasi-linearization techniques for the periodic Riccati equation, and the design of receding-horizon control strategies for periodic and multirate systems. When specialized to time-invariant systems, the results give rise to new sufficient conditions for the cyclomonotonicity of the solutions of the time-invariant Riccati equation and the existence of periodic stabilizing feedback

Keywords

Kalman filters; difference equations; discrete time systems; feedback; linear systems; matrix algebra; stability; time-varying systems; Kalman filter; cyclomonotonicity; difference periodic Riccati equation; discrete-time linear T-periodic system; filter design; initial covariance matrix; multirate systems; periodic filter; periodic stabilizing feedback; quasi-linearization techniques; receding-horizon control strategies; stabilizability; time-invariant Riccati equation; Control systems; Covariance matrix; Difference equations; Electrons; Kalman filters; Optical sensors; Radar detection; Riccati equations; Sensor systems; Sufficient conditions;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.159582

Filename

159582