A note on the maximal solution of the periodic Riccati equation

Author

Bittanti, Sergio ; Colaneri, Patrizio ; De Nicolao, Giuseppe

Author_Institution

Dept. of Electron., Polytech. of Milan, Italy

Volume

34

Issue

12

fYear

1989

fDate

12/1/1989 12:00:00 AM

Firstpage

1316

Lastpage

1319

Abstract

The periodic symmetric solutions of the periodic Riccati differential equation associated with the filtering problem are considered by the authors. It is proven that, under the sole assumption of detectability, there exists a maximal solution. Moreover, such a solution turns out to be strong, i.e. the characteristic multipliers of the associated closed-loop system belong to the closed unit disk. The proof relies on an iterative linearization technique, which calls for a sequence of periodic Lyapunov equations. Similar results are given for the minimal solution

Keywords

closed loop systems; differential equations; filtering and prediction theory; iterative methods; linearisation techniques; closed-loop system; detectability; differential equation; filtering; iterative linearization technique; maximal solution; minimal solution; periodic Lyapunov equations; periodic Riccati equation; periodic symmetric solutions; Controllability; Councils; Differential equations; Filtering; Linearization techniques; Observability; Optimal control; Performance analysis; Riccati equations; Scanning probe microscopy;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.40785

Filename

40785