Trading the stability of finite zeros for global stabilization of nonlinear cascade systems

Author

Sepulchre, Rodolphe ; Arcak, Murat ; Teel, Andrew R.

Author_Institution

Inst. Montefiore, Univ. de Liege, Liege Sart-Tilman, Belgium

Volume

47

Issue

3

fYear

2002

fDate

3/1/2002 12:00:00 AM

Firstpage

521

Lastpage

525

Abstract

Analyzes the stabilizability properties of nonlinear cascades in which a nonminimum phase linear system is interconnected through its output to a stable nonlinear system. It is shown that the instability of the zeros of the linear system can be traded with the stability of the nonlinear system up to a limit fixed by the growth properties of the cascade interconnection term. Below this limit, global stabilization is achieved by smooth static-state feedback. Beyond this limit, various examples illustrate that controllability of the cascade may be lost, making it impossible to achieve large regions of attractions

Keywords

asymptotic stability; cascade systems; controllability; linear systems; matrix algebra; nonlinear control systems; poles and zeros; state feedback; cascade interconnection; controllability; finite zeros; global stabilization; growth properties; nonlinear cascade systems; nonminimum phase linear system; regions of attraction; smooth static-state feedback; stability; stabilizability properties; stable nonlinear system; Automatic control; Control systems; Linear matrix inequalities; Linear systems; Nonlinear systems; Riccati equations; Stability; Stochastic processes; Sufficient conditions; Symmetric matrices;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.989153

Filename

989153