Nonsquare spectral factorization for nonlinear control systems

Author

Petersen, Mark A. ; Van Der Schaft, Arjan J.

Author_Institution

Dept. of Math. & Appl. Math., North-West Univ., Potchefstroom, South Africa

Volume

50

Issue

3

fYear

2005

fDate

3/1/2005 12:00:00 AM

Firstpage

286

Lastpage

298

Abstract

This paper considers nonsquare spectral factorization of nonlinear input affine state space systems in continuous time. More specifically, we obtain a parametrization of nonsquare spectral factors in terms of invariant Lagrangian submanifolds and associated solutions of Hamilton-Jacobi inequalities. This inequality is a nonlinear analogue of the bounded real lemma and the control algebraic Riccati inequality. By way of an application, we discuss an alternative characterization of minimum and maximum phase spectral factors and introduce the notion of a rigid nonlinear system.

Keywords

Riccati equations; continuous time systems; matrix decomposition; nonlinear control systems; state-space methods; Hamilton-Jacobi inequalities; bounded real lemma; control algebraic Riccati inequality; invariant Lagrangian submanifolds; nonlinear control systems; nonlinear input affine state space systems; nonsquare spectral factorization; rigid nonlinear system; Chemical processes; Control systems; Control theory; Lagrangian functions; Nonlinear control systems; Nonlinear equations; Nonlinear systems; Process control; Riccati equations; Stochastic processes; Hamilton–Jacobi inequalities; invariant Lagrangian manifolds; nonlinear nonsquare spectral factors;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2005.843845

Filename

1406124