Skip to main content
Open Access Publications from the University of California

UC Santa Cruz

UC Santa Cruz Previously Published Works bannerUC Santa Cruz

Inter-event Times Analysis for Planar Linear Event-triggered Controlled Systems

  • Author(s): Postoyan, R;
  • Sanfelice, RG;
  • Heemels, WPMH
  • et al.

We analyse the properties of the inter-event times for planar linear time-invariant systems controlled by an event-triggered state-feedback law. The triggering rule is given by the relative threshold strategy and we assume that the tunable triggering parameter is small. Several cases are distinguished depending on the nature of the eigenvalues of the (continuous-time) closed-loop system matrix in absence of sampling. When these eigenvalues are real, it is shown that the inter-event times lie in a neighborhood of a given constant for all positive times or converge to the neighborhood of a given constant as time grows. When the eigenvalues are complex conjugates, the inter-event times oscillate with a varying period for which we give an estimate. Moreover, the values taken by the inter-event times over this varying period are approximately the same for all initial conditions. As a consequence, one can run a single simulation over a given interval of time to infer properties of the inter-event times for all initial conditions and all positive times. Numerical simulations are provided to support the presented theoretical guarantees. These results help to understand the behaviour of the inter-event times, instead of solely relying on numerical simulations, and can be exploited to evaluate the performance of the considered triggering condition in terms of average inter-transmission times.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Main Content
For improved accessibility of PDF content, download the file to your device.
Current View