A Small-Gain Approach to Robust Event-Triggered Control of Nonlinear Systems

Tengfei Liu, Zhong Ping Jiang

Research output: Contribution to journalArticlepeer-review


This paper presents a new approach to event-triggered control for nonlinear uncertain systems by using the notion of input-to-state stability (ISS) and the nonlinear small-gain theorem. The contribution of this paper is threefold. First, it is proved that infinitely fast sampling can be avoided if the system is input-to-state stabilizable with the sampling error as the external input and the corresponding ISS gain is locally Lipschitz. 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 using ISS small-gain arguments. Second, the proposed approach gives rise to a new self-triggered sampling strategy for a class of nonlinear systems subject to external disturbances. If an upper bound of the external disturbance is known, then the closed-loop system can be designed to be robust to the external disturbance, and moreover, the system state globally asymptotically converges to the origin if the external disturbance decays to zero. Third, a new design method is developed for event-triggered control of nonlinear uncertain systems in the strict-feedback form. It is particularly shown that the ISS gain with the sampling error as the input can be designed to satisfy the proposed condition for event-triggered control and self-triggered control.

Original languageEnglish (US)
Article number7027161
Pages (from-to)2072-2085
Number of pages14
JournalIEEE Transactions on Automatic Control
Issue number8
StatePublished - Aug 1 2015


  • Cyclic-small-gain theorem
  • event-triggered control
  • input-to-state stability (ISS)
  • nonlinear systems
  • robust control

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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