### 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.

Original language | English |
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Title of host publication | Nonlinear systems |

Subtitle of host publication | techniques for dynamical analysis and control |

Editors | N. Wouw, van de, E. Lefeber, I. Lopez Arteaga |

Place of Publication | Berlin |

Publisher | Springer |

Pages | 51-77 |

Number of pages | 27 |

ISBN (Print) | 9783319303567 |

DOIs | |

Publication status | Published - 2017 |

Event | International workshop on Nonlinear Systems in honor of Henk Nijmeijer’s 60th birthday, 2016 - Eindhoven, Netherlands Duration: 21 Jan 2016 → 21 Jan 2016 |

### Publication series

Name | Lecture Notes in Control and Information Sciences |
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Volume | 470 |

ISSN (Print) | 01708643 |

### Conference

Conference | International workshop on Nonlinear Systems in honor of Henk Nijmeijer’s 60th birthday, 2016 |
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Country | Netherlands |

City | Eindhoven |

Period | 21/01/16 → 21/01/16 |

### Fingerprint

### Cite this

*Nonlinear systems: techniques for dynamical analysis and control*(pp. 51-77). (Lecture Notes in Control and Information Sciences; Vol. 470). Berlin: Springer. https://doi.org/10.1007/978-3-319-30357-4_3

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*Nonlinear systems: techniques for dynamical analysis and control.*Lecture Notes in Control and Information Sciences, vol. 470, Springer, Berlin, pp. 51-77, International workshop on Nonlinear Systems in honor of Henk Nijmeijer’s 60th birthday, 2016, Eindhoven, Netherlands, 21/01/16. https://doi.org/10.1007/978-3-319-30357-4_3

**Convergent systems : nonlinear simplicity.** / Pavlov, A.; van de Wouw, N.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

TY - CHAP

T1 - Convergent systems

T2 - nonlinear simplicity

AU - Pavlov, A.

AU - van de Wouw, N.

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84978524315&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-30357-4_3

DO - 10.1007/978-3-319-30357-4_3

M3 - Chapter

AN - SCOPUS:84978524315

SN - 9783319303567

T3 - Lecture Notes in Control and Information Sciences

SP - 51

EP - 77

BT - Nonlinear systems

A2 - Wouw, van de, N.

A2 - Lefeber, E.

A2 - Lopez Arteaga, I.

PB - Springer

CY - Berlin

ER -