Zubov's method for interconnected systems - a dissipative formulation

H. Li, F. Wirth: Zubov's method for interconnected systems - a dissipative formulation
in: Proceedings on the 20th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2012), July 9-13, 2012, Melbourne, Australia, Melbourne, Australia, 2012, 8 pages, CD-ROM, Paper No. 184, full paper

ISBN/ISSN/ISMV Nummer: 978-0-646-58062-3
Keywords: nonlinear systems; input-to state stability (ISS); integral input-to state stability (iISS); ISS Lyapunov function; small gain condition; Zubov's method
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Abstract:

We study the domain of attraction of an asymptotically stable fixed point of the feedback interconnections of two nonlinear systems. For each subsystem we introduce an auxiliary system and assume that it is uniformly locally asymptotically stable at the origin. It is then shown that each subsystem is integral input-to state stable(iISS) regarding the state of the other subsystem as input. If the interconnection of the two subsystems satisfies a small gain condition, an estimate for the domain of attraction of the whole system may be obtained by constructing a nonsmooth Lyapunov function.

Contents:

1. Introduction
1.1 Preliminaries
1.2 The auxiliary system
2. Main Results
2.1 The domain of attraction of the auxiliary system
2.2 Coupled Systems
  Conclusions

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