Stabilization of linear systems with time‐varying input delay by event‐triggered delay independent truncated predictor feedback

Abstract

This paper deals with the problem of stabilization of linear systems with time-varying input delay by an event-triggered delay independent truncated predictor feedback law, either of the state feedback type or the output feedback type. Only the information of a delay bound rather than the delay itself is required in the design of both control laws and event-triggering strategies. For both the state feedback case and the output feedback case, an admissible delay bound that guarantees the stabilizability of a general linear system is established, and the Zeno behavior is shown to be excluded. For linear systems with all open loop poles at the origin or in the open left-half plane, stabilization can be achieved for a delay under an arbitrarily large bound.

Predictor-based control of time-delay systems: a survey

“…In , the output-feedback truncated predictor-based controllers are proposed for LTI discrete-time systems with single known/unknown time-varying input delay. In (Xie, Wei, & Lin, 2020), the event-triggered mechanism was combined with the truncated predictor-based controller for reducing the computational load when stabilising an LTI TDS with a time-varying input delay.…”

“…Such a protocol brings in the capacity to determine the most indispensable execution instants of sensing/controlling: the sensor measurements/control law updates will only be permitted when some predetermined switching conditions are satisfied. For linear systems, the event-triggered predictor-based control has been conducted in (Selivanov & Fridman, 2016bZhu & Fridman, 2021) through the continuous-time approach and Yang & Zheng, 2019;Léchappé et al, 2019;Xie et al, 2020;González, 2021) by means of the discrete-time method. More recently, the authors of (Nozari, Tallapragada, & Cortés, 2020;Sun, Yang, & Zeng, 2022) developed event-triggered predictor-based controllers for nonlinear TDSs with time-varying delays or model uncertainties.…”

Global Asymptotic Stabilization of Feedforward Systems with an Uncertain Delay in the Input by Event-Triggered Control

“…In [4], an adaptive event-trigged control was proposed for uncertain nonlinear systems. Then, in [1], [8], [9], [12], there were various results of event-triggered control for input-delayed linear systems where the input delay is either constant, or time-varying but known. Up to now, based on our survey, there have been much less results on event-triggered control for input-delayed feedforward systems.…”

Delay effects on the mean‐square stabilization of stochastic systems with input delay

“…Numerous articles on delay systems assume that the delay, including constant delay and time‐varying delay, is fixed 9‐13 . Other articles involve delay effects on stability, convergence rate, consensus, and so on 14‐16 .…”

“…Numerous articles on delay systems assume that the delay, including constant delay and time-varying delay, is fixed. [9][10][11][12][13] Other articles involve delay effects on stability, convergence rate, consensus, and so on. [14][15][16] Frequency domain methods were utilized to study delay margin problems, which aim to determine the largest time delay 𝜏 max , such that for any 𝜏 < 𝜏 max , there exists a linear time-invariant controller that stabilizes the delay system for any delay in [0, 𝜏]; 14,17,18 Delay effects on stability were considered and delay ranges within which systems are stable were characterized in References 19 and 20; The effect of delay on the convergence rate of a retarded delay system was studied via the Lambert W function by Reference 21; A consensus protocol for multi-agent systems subject to communication delays was proposed and a delay range within which the systems achieve consensus was presented in Reference 15.…”