Complete type Lyapunov functionals for integral delay systems with multiple delays

Melchor-Aguilar, Daniel; Arismendi-Valle, Héctor

doi:10.1002/rnc.5737

Cited by 4 publications

(1 citation statement)

References 28 publications

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“…Finally, an appealing research avenue is the study of the class of manifolds that emerges from the corresponding complete type functional of distributed, neutral, 20 and periodic systems, 26 or of the systems described by integral 27,28 and delay difference equations. 29…”

Section: Discussionmentioning

confidence: 99%

Closing the gap from nominal to robust asymptotic stabilization of time delay systems

Gomez,

Cruz‐Ancona

2024

Intl J Robust & Nonlinear

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SummaryThe control problem of a general class of perturbed linear invariant time‐delay systems within the Sliding Mode Control framework is addressed. We introduce a novel class of sliding manifolds with a structure not previously reported in the literature, which constructively emerges from complete type functionals of the corresponding nominal time‐delay systems and depends on the whole state of the system. A fundamental conclusion derived from this proposal is that every time‐delay system with matched perturbations, whose associated nominal system is exponentially stabilizable, is robustly asymptotically stabilizable. In fact, the introduced sliding manifold enables to construct discontinuous and continuous sliding mode control‐based algorithms that mitigate different classes of perturbations.

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