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ON NONLINEAR INNER SYSTEMS AND CONNECTIONS WITH CONTROL THEORY
Mark A. Petersen* Arjan J. van der Schaft**
* Department of Mathematics & Applied Mathematics,
Potchefstroom University, Potchefstroomc 6001, Potchefstroom
2520, South Africa, e-mail: wskmap@puknet.puk.ac.za
** Faculty of Mathematical Sciences, University of Twente, P.O.
Box 217, 7500 AE Enschede, the Netherlands, e-mail:
a.j.vanderschaft@math.utwente.nl
This paper extends some results involving linear inner systems to the nonlinear case. In thsi regard, the arithmetic of nonlinear inner systems is developed further and some new connections with nonlinear spectral and all-pass factorization and control theory are discussed. In particular, explicit formulas for the (state space) realizations of nonlinear inner systems in terms of the components of extremal spectral factors is provided. Relationships between inner systems and process control, geometric control and H∞ control are also discussed.
Keywords: Nonlinear Inner Systems; Spectral Factorization; Process, Geometric, and H-infinity Control
Session slot T-Mo-M08: Analysis of Nonlinear Systems/Area code 2c : Non-linear Systems
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