Lyapunov Design for Event-Triggered Exponential Stabilization
This provides a theoretical guarantee for bridging continuous-time CLF designs to practical digital implementations without significant performance loss.
The paper proves that for any continuous-time controller providing exponential stabilization via a Control Lyapunov Function, an event-triggered implementation exists that achieves exponential stability with a convergence rate arbitrarily close to the continuous-time rate.
Control Lyapunov Functions (CLF) method gives a constructive tool for stabilization of nonlinear systems. To find a CLF, many methods have been proposed in the literature, e.g. backstepping for cascaded systems and sum of squares (SOS) programming for polynomial systems. Dealing with continuous-time systems, the CLF-based controller is also continuous-time, whereas practical implementation on a digital platform requires sampled-time control. In this paper, we show that if the continuous-time controller provides exponential stabilization, then an exponentially stabilizing event-triggered control strategy exists with the convergence rate arbitrarily close to the rate of the continuous-time system.