A spectral test for observability and reachability of time-varying systems and the Riccati difference equation

Author

Peters, M.A. ; Iglesias, P.A.

Author_Institution

Philips Res. Lab., Eindhoven, Netherlands

Volume

3

fYear

1999

fDate

1999

Firstpage

2727

Abstract

A spectral test for the observability and reachability of linear time-invariant systems-the PBH (Popov-Belevitch-Hautus) test-is well-known and serves to be a powerful characterization of these properties. In this paper, it is shown that similar tests exist for linear time-varying systems involving a check over a subset of the spectrum of the weighted block shift, known as the `set of almost eigenvalues´. These tests are then used to derive necessary and sufficient conditions for the existence of a stabilizing solution to the Riccati difference equation of quadratic optimal control

Keywords

Riccati equations; difference equations; eigenvalues and eigenfunctions; linear systems; observability; optimal control; quadratic programming; reachability analysis; spectral analysis; stability; time-varying systems; PBH test; Popov-Belevitch-Hautus test; Riccati difference equation; almost eigenvalues; linear time-varying systems; necessary conditions; observability; quadratic optimal control; reachability; spectral test; stabilizing solution; sufficient conditions; weighted block shift; Difference equations; Eigenvalues and eigenfunctions; Hilbert space; Observability; Optimal control; Riccati equations; Stability; Sufficient conditions; System testing; Time varying systems;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1999. Proceedings of the 38th IEEE Conference on

Conference_Location

Phoenix, AZ

ISSN

0191-2216

Print_ISBN

0-7803-5250-5

Type

conf

DOI

10.1109/CDC.1999.831342

Filename

831342