Exponential input-to-state stability of globally Lipschitz time-delay systems under sampled-data noisy output feedback and actuation disturbances

Ferdinando, Mario Di; Pepe, Pierdomenico; Fridman, Emilia

doi:10.1080/00207179.2019.1662949

Cited by 17 publications

(5 citation statements)

References 55 publications

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“…The usual Halanay's inequality result [8] is the following: if a > b, then v(t) exponentially converges to zero as t → +∞. In addition to our works [16] and [17] that relax the requirement that the decay rate a is strictly larger than the gain b, several other extensions of this result are available in the literature e.g., in [6], [20], [23], and [24]. Time-varying versions have been studied in [2] and [15].…”

Section: Introductionmentioning

confidence: 72%

Vector Extensions of Halanay’s Inequality

Mazenc

Malisoff

Krstić

2022

IEEE Trans. Automat. Contr.

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We provide two extensions of Halanay's inequality, where the scalar function in the usual Halanay's inequality is replaced by a vector valued function, under a Metzler condition. We provide an easily checked necessary and sufficient condition for asymptotic convergence of the function to the zero vector in the time invariant case. For time-varying cases, we provide a sufficient condition for this convergence, which can be easily checked when the systems are periodic. We illustrate our results in cases that are beyond the scope of prior asymptotic stability results.

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Section: Introductionmentioning

confidence: 72%

Vector Extensions of Halanay’s Inequality

Mazenc

Malisoff

Krstić

2022

IEEE Trans. Automat. Contr.

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“…Existing results give conditions for the preservation of the stability -in a certain sense-of the CT closed-loop system when implemented in a sampled-data setting (Pepe and Fridman, 2017;Lin, 2020;Lin and Wei, 2018;Di Ferdinando and Pepe, 2019;Lin and Sun, 2021;Di Ferdinando et al, 2021a). In particular, sampled-data stabilization under nonuniform sampling has lately been an active research topic (Li and Zhao, 2018;Hetel et al, 2017;Omran et al, 2016).…”

Section: Introductionmentioning

confidence: 99%

Linking stability of nonlinear sampled-data systems and their continuous-time limits

Vallarella¹,

Haimovich²

2022

Preprint

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Discrete-time (DT) models of sampled-data systems can be regarded as predictions of the future state value given current values for the state, input and sampling period. A DT model is exact if its prediction coincides with the true value and is otherwise approximate. Conditions under which Semiglobal Exponential Stability under nonuniform sampling (SES-VSR) is preserved among different (exact or approximate) DT models when fed back with the same sampling-period dependent control law exist. The current paper proves that the exact DT model is SES-VSR if and only if its corresponding continuous-time (CT) limit (for infinitesimally small sampling period) is Globally Exponentially Stable (GES), which is restrictive. The contribution of this note consists in extending and relaxing the assumptions of previous results, as follows: (i) only mild conditions are given in order to link stability properties between DT models fed back with different control laws, and (ii) the DT model properties making the CT limit Globally Asymptotically and Locally Exponentially Stable (GALES), instead of GES, are provided.

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“…On sampled-value control for systems with disturbance, there are two major control approaches; sliding mode control [9][10][11] and disturbance observer-based control [12,13]. Additionally, control error evaluation method based on input-to-state stability was proposed [14].…”

Section: Introductionmentioning

confidence: 99%

“…Time-dependent disturbances can cause steady-state errors in feedback control systems and, generally, static feedback controllers cannot guarantee asymptotic stability. Owing to their importance in practical situations, the time-dependent disturbance has been extensively investigated for continuous-time and periodic sampled-value feedback systems [9][10][11][12][13][14], but the problem remains unresolved for aperiodic sampled-data feedback systems. In [30,31], the disturbance was assumed to be bounded by a norm of system states, time-dependent disturbance cannot be considered by the approach in [30,31].…”

Section: Introductionmentioning

confidence: 99%

Local robust stability on compact set for nonlinear systems with continuous time controller against to aperiodic sampling and disturbance

Umemoto

Endo

Matsuno

2022

IET Control Theory & Appl

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In this study, the stability of a sampled-value control system with time-and state-dependent disturbance and aperiodic sampling is investigated. To expand the application class of the sampled-value controller, the local stability on a compact set is considered under the assumption of local Lipschitz continuity on the compact set. Because the assumption is weaker than the global Lipschitz continuity, the proposed stability analysis is applicable to a wider class of controlled systems. Global stability under the assumption of global Lipschitz continuity is also considered. The effectiveness of the derived stability condition is verified by conducting numerical simulations with some control parameters variations such as the disturbance magnitude and sample interval.

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Exponential input-to-state stability of globally Lipschitz time-delay systems under sampled-data noisy output feedback and actuation disturbances

Cited by 17 publications

References 55 publications

Vector Extensions of Halanay’s Inequality

Vector Extensions of Halanay’s Inequality

Linking stability of nonlinear sampled-data systems and their continuous-time limits

Local robust stability on compact set for nonlinear systems with continuous time controller against to aperiodic sampling and disturbance

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