On the Local Input–Output Stability of Event-Triggered Control Systems

This paper studies performance preserving event design in nonlinear event-based control systems based on a local L2-type performance criterion. Considering a finite gain local L2-stable disturbance driven continuous-time system, we propose a triggering mechanism so that the resulting sampled-data system preserves similar disturbance attenuation local L2-gain property. The results are applicable to nonlinear systems with exogenous disturbances bounded by some Lipschitz-continuous function of state. It is shown that an exponentially decaying function of time, combined with the proposed triggering condition, extends the interevent periods. Compared to the existing works, this paper analytically estimates the increase in intersampling periods at least for an arbitrary period of time. We also propose a so-called discrete triggering condition to quantitatively find the improvement in interevent times at least for an arbitrary number of triggering iterations. Illustrative examples support the analytically derived results.