Cited by 21Stability and Control of Uncertain SystemsControl and Stability of Dynamical SystemsAdaptive Control of Nonlinear Systems

Global Input Delay Tolerance of MIMO Nonlinear Systems under Nonsmooth Feedback: A Homogeneous Perspective

Yu, Xin, Lin, Wei·2022·IEEE Transactions on Automatic Control

Abstract

In this paper, we tackle the problem of when a globally asymptotically stabilizable (GAS) nonlinear system by either state or output feedback is globally tolerable with respect to input delay. We focus on the case when the continuous system is not stabilizable by linear or smooth feedback, and thus local exponential stabilizability (LES) is not fulfilled. With the aid of the Lyapunov-Krasovskii functional method and weighted homogeneity, we prove that for a multi-input-multi-output (MIMO) nonlinear system with homogeneous degree zero, global asymptotic stabilizability by nonsmooth but Hölder continuous state or output feedback implies global asymptotic stability (GAS) of the closed-loop system with input delay, i.e., the property of global input delay tolerance (GIDT). We then illustrate applications of the obtained GIDT results to significant classes of time-delay nonlinear systems with uncontrollable/unobservable linearization, including but not limited to a chain of nonlinear integrators, higher-order systems with a lower-triangular or upper-triangular structure, and beyond.

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Crossref · 10.1109/tac.2022.3197558

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Research works printed but not linked: 5

  1. hardy, 1952, Inequalities
  2. hermes, 1991, Homogeneous coordinates and continuous asymptotically stabilizing feedback controls, Differential Equations, 127, 249
  3. kawski, 1990, Homogeneous stabilizing feedback laws, Control Theory Adv Technol, 6, 497
  4. j, 1956, On the inversion of Lyapunov's second theorem on the stability of motion, Amer Math Soc Trans, 24, 19
  5. kawski, 0, Geometric homogeneity and applications to stabilization, Proc 3rd IFAC Symp Nonlinear Control Syst, 164

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Authors
Yu, X., & Lin, W.
Affiliations
Case Western Reserve University (US)
Venue
IEEE Transactions on Automatic Control
Published
2022
Pages
1-16
ISSN
  • 0018-9286 (ISSN-L)
  • 1558-2523
  • 2334-3303
OpenAlex
W4301122491
Cited by
21
References
51
Citations by year
2026: 3 · 2025: 2 · 2024: 8 · 2023: 6 · 2022: 2
FWCI
1.82
Type
journal article
Language
en
Open access
closed
Locations
IEEE Transactions on Automatic Control (publishedVersion)
Topics
  • Physical Sciences › Engineering › Control and Systems Engineering › Stability and Control of Uncertain Systems
  • Physical Sciences › Engineering › Control and Systems Engineering › Control and Stability of Dynamical Systems
  • Physical Sciences › Engineering › Control and Systems Engineering › Adaptive Control of Nonlinear Systems
Keywords
MIMO nonlinear systems, global asymptotic stabilization, Lyapunov-Krasovskii functional, time-delay systems, lower triangular systems, upper-triangular systems

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