J-inner-outer factorization, J-spectral factorization, and robust control for nonlinear systems

Author

Ball, Joseph A. ; Van Der Schaft, Arjan J.

Author_Institution

Dept. of Math., Virginia Polytech. Inst. & State Univ., Blacksburg, VA, USA

Volume

41

Issue

3

fYear

1996

fDate

3/1/1996 12:00:00 AM

Firstpage

379

Lastpage

392

Abstract

The problem of expressing a given nonlinear state-space system as the cascade connection of a lossless system and a stable, minimum-phase system (inner-outer factorization) is solved for the case of a stable system having state-space equations affine in the inputs. The solution is given in terms of the stabilizing solution of a certain Hamilton-Jacobi equation. The stable, minimum-phase factor is obtained as the solution of an associated nonlinear spectral factorization problem. As an application, one can arrive at the solution of the nonlinear H_∞-control problem for the disturbance feedforward case

Keywords

matrix decomposition; nonlinear control systems; robust control; state-space methods; H_∞-control problem; Hamilton-Jacobi equation; J-inner-outer factorization; J-spectral factorization; cascade connection; disturbance feedforward; lossless system; nonlinear spectral factorization problem; nonlinear systems; robust control; stable minimum-phase system; state-space system; Chemical processes; Differential equations; Discrete time systems; IEEE news; Mathematics; Nonlinear dynamical systems; Nonlinear equations; Nonlinear systems; Process control; Robust control;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.486639

Filename

486639