### Abstract

This chapter studies the event-triggered control problem for nonlinear systems with input-to-state stability (ISS) as the basic notion and the ISS small-gain theorem as a tool. The contribution of this book chapter is threefold. First, an ISS gain condition is proposed for event-triggered control of nonlinear uncertain systems. It is proved that infinitely fast sampling can be avoided with an appropriately designed event triggering mechanism if the system is input-to-state stabilizable with measurement error as the external input and the resulted ISS gain is Lipschitz on compact sets. No assumption on the existence of known ISS-Lyapunov functions is made in the discussions. Moreover, the forward completeness problem with event-triggered control is studied systematically by ISS small-gain arguments. Self-triggered control designs for systems under external disturbance are also developed in the ISS-based framework. Second, this chapter introduces a new design method for input-to-state stabilization of nonlinear uncertain systems in the strict-feedback form. It is particularly shown that the ISS gain with the measurement error as the input can be designed to satisfy the proposed condition for event-triggered control.

Original language | English (US) |
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Title of host publication | Systems Theory |

Subtitle of host publication | Perspectives, Applications and Developments |

Publisher | Nova Science Publishers, Inc. |

Pages | 49-76 |

Number of pages | 28 |

ISBN (Electronic) | 9781631178764 |

ISBN (Print) | 9781631178665 |

State | Published - Apr 1 2014 |

### Keywords

- Full-State feedback
- Input-To-state Stability
- Nonlinear Small-Gain theorem
- Nonlinear systems
- Partial-State feedback
- Uncertainty
- Vent-Triggered control

### ASJC Scopus subject areas

- Arts and Humanities(all)

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## Cite this

*Systems Theory: Perspectives, Applications and Developments*(pp. 49-76). Nova Science Publishers, Inc..