Sampled‐data implementation of extended PID control using delays

Abstract

AbstractWe study the sampled‐data implementation of extended PID control using delays for the nth‐order stochastic nonlinear systems. The derivatives are approximated by finite differences giving rise to a delayed sampled‐data controller. An appropriate Lyapunov–Krasovskii (L‐K) method is presented to derive linear matrix inequalities (LMIs) for the exponential stability of the resulting closed‐loop system. We show that with appropriately chosen gains, the LMIs are always feasible for small enough sampling period and stochastic perturbation. We further employ an event‐triggering condition that allows to reduce the number of sampled control signals used for stabilization and provide ‐gain analysis. Finally, three numerical examples illustrate the efficiency of the presented approach.