Simple conditions for sampled-data stabilization by using artificial delay

Abstract

It is well known that in some systems a stabilizing feedback that depends on the output and its derivative can be replaced by delay-dependent feedback where the derivative is approximated by a finite difference. We study sampled-data implementation of such delay-dependent feedback. The analysis is based on the Taylor representation of the delayed signal with the remainder in the integral form, which is then compensated by appropriate Lyapunov-Krasovskii functional. This allows to obtain simple LMI-based conditions guaranteeing a desired decay rate of convergence. Using these conditions, we prove that if the system can be stabilized by continuous-time derivative-dependent feedback then it can be stabilized by sampled-data delay-dependent feedback with small enough sampling and delay. Finally, we introduce the event-triggering mechanism that allows to reduce the amount of transmitted signals at the cost of larger memory used.