Sufficient conditions for minimality of a nonlinear realization via controllability and observability functions

Author

Scherpen, Jacquelien M A ; Gray, W. Steven

Author_Institution

Dept. of Electr. Eng., Delft Univ. of Technol., Netherlands

Volume

6

fYear

1998

fDate

21-26 Jun 1998

Firstpage

3349

Abstract

We develop a set of sufficient conditions in terms of controllability and observability functions under which a given state space realization of a formal power series is minimal. Specifically, it is shown that positivity of these functions, plus a few technical conditions, implies minimality. In doing so, connections are established between Hamilton-Jacobi type optimal control theory and the well known necessary and sufficient conditions for minimality in terms of Kalman type rank conditions on the accessibility and observability distributions

Keywords

controllability; nonlinear control systems; observability; optimal control; series (mathematics); Hamilton-Jacobi type optimal control theory; Kalman type rank conditions; accessibility; formal power series; minimality; necessary and sufficient conditions; nonlinear realization; state space realization; sufficient conditions; Controllability; Kalman filters; Linear systems; Observability; Optimal control; Power engineering and energy; Power engineering computing; Reduced order systems; State-space methods; Sufficient conditions;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference, 1998. Proceedings of the 1998

Conference_Location

Philadelphia, PA

ISSN

0743-1619

Print_ISBN

0-7803-4530-4

Type

conf

DOI

10.1109/ACC.1998.703195

Filename

703195