State-dependent sampling for perturbed time-delay systems

In this work we present a state-dependent sampling control that allows for enlarging the sampling intervals of state-feedback control. We consider the case of perturbed linear time-invariant systems with input-delay and guarantee their ℒ₂-stability. The approach is based on a novel class of switched Lyapunov-Krasovskii functionals with state-dependent matrices. It results in an LMI problem that allows for enlarging the sampling interval according to the system state. Then, a mapping of the state space is designed offline: it computes for each state of the state space a lower-bound estimation of the maximum allowable sampling interval, which makes it possible to reduce the number of actuations during the real-time control of the system.