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Erschienen in:
Controlled Invariant Distributions and Differential Properties Kapitel lesen Erstes Kapitel lesen

2017 | OriginalPaper | Buchkapitel

3. Convergent Systems: Nonlinear Simplicity

verfasst von : Alexey Pavlov, Nathan van de Wouw

Erschienen in: Nonlinear Systems

Verlag: Springer International Publishing

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Abstract

Convergent systems are systems that have a uniquely defined globally asymptotically stable steady-state solution. Asymptotically stable linear systems excited by a bounded time varying signal are convergent. Together with the superposition principle, the convergence property forms a foundation for a large number of analysis and (control) design tools for linear systems. Nonlinear convergent systems are in many ways similar to linear systems and are, therefore, in a certain sense simple, although the superposition principle does not hold. This simplicity allows one to solve a number of analysis and design problems for nonlinear systems and makes the convergence property highly instrumental for practical applications. In this chapter, we review the notion of convergent systems and its applications to various analyses and design problems within the field of systems and control.

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Vorheriges Kapitel Some Recent Results on Distributed Control of Nonlinear Systems
Nächstes Kapitel Synchronisation and Emergent Behaviour in Networks of Heterogeneous Systems: A Control Theory Perspective
Fußnoten
1
For simplicity, in this chapter, we consider only continuous-time systems with locally Lipschitz right-hand sides. Definitions and basic results for discrete-time systems and for continuous-time systems with discontinuous right-hand sides can be found in [18, 36, 38, 39, 56].
 
2
A more general definition of convergent systems, where the steady-state solution has an arbitrary domain of attraction (not necessarily global as in this chapter) can be found in [35].
 
3
See [48] for a definition of the input-to-state stability property.
 
4
This result is a particular case of a more general condition on \(G_{yu}(j\omega )\) in the form of Circle criterion [56].
 
5
This benefit has recently also been explicitly recognized in [13].
 
6
These results were obtained in parallel with [21], where an alternative approach to nonlocal nonlinear output regulation problem was pursued.
 
7
Other variants of the uniform output regulation problem can be found in [35].
 
8
Sufficient smoothness of the functions f, h and \(\alpha \) is assumed.
 
9
In fact, a particular Lyapunov-based stability certificate is required for the solution \(\bar{x}_{\theta ,w}(t)\) in the scope of this section, see [17].
 
10
The model reduction approach described here is based on [6].
 
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Metadaten
Titel
Convergent Systems: Nonlinear Simplicity
verfasst von
Alexey Pavlov
Nathan van de Wouw
Copyright-Jahr
2017
Buch
Nonlinear Systems

Print ISBN: 978-3-319-30356-7

Electronic ISBN: 978-3-319-30357-4

Copyright-Jahr: 2017

DOI
https://doi.org/10.1007/978-3-319-30357-4_3

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