Using exponential time-varying gains for sampled-data stabilization and estimation

Ahmed‐Ali, Tarek; Fridman, Emilia; Giri, F.; Burlion, Laurent; Lamnabhi‐Lagarrigue, Françoise

doi:10.1016/j.automatica.2016.01.048

Cited by 87 publications

(44 citation statements)

References 14 publications

(17 reference statements)

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“…Therefore, there exists a constantC such that ẑ(•, t) H 1≤C w(•, t) H 1 (21) ≤CC w e − min{αo,αc}t z(•, 0) H 1 for t ≥ t 0 . Since z(x, t) =ẑ(x, t − r) −z(x, t), the latter together with (5) imply (22).…”

Section: Using Integration By Parts We Havėmentioning

confidence: 97%

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Delayed boundary control of a heat equation under discrete-time point measurements

Selivanov

Fridman

2017

2017 IEEE 56th Annual Conference on Decision and Control (CDC)

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Section: Using Integration By Parts We Havėmentioning

confidence: 97%

“…In [21] a time-varying injection gain was introduced in the observer to improve its exponential convergence under delayed measurements. This result was revisited in [22] to increase the period of a sampled-data system.…”

Section: Introductionmentioning

confidence: 99%

Delayed boundary control of a heat equation under discrete-time point measurements

Selivanov

Fridman

2017

2017 IEEE 56th Annual Conference on Decision and Control (CDC)

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“…By using the inequality (12) in Lemma 2 and considering (49) and [x 2v−1 ,x 2v ] ⊂ [x v , x v+1 ], we get for any v ∈ M,…”

Section: Appendix C Proof Of Theoremmentioning

confidence: 99%

Spatially Piecewise Fuzzy Control Design for Sampled-Data Exponential Stabilization of Semilinear Parabolic PDE Systems

Wang

Tsai

et al. 2018

IEEE Trans. Fuzzy Syst.

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This paper employs a Takagi-Sugeno (T-S) fuzzy partial differential equation (PDE) model to solve the problem of sampled-data exponential stabilization in the sense of spatial L ∞ norm ∥ · ∥∞ for a class of nonlinear parabolic distributed parameter systems (DPSs), where only a few actuators and sensors are discretely distributed in space. Initially, a T-S fuzzy PDE model is assumed to be derived by the sector nonlinearity method to accurately describe complex spatiotemporal dynamics of the nonlinear DPSs. Subsequently, a static sampled-data fuzzy local state feedback controller is constructed based on the T-S fuzzy PDE model. By constructing an appropriate Lyapunov-Krasovskii functional candidate and employing vector-valued Wirtinger's inequalities, a variation of vector-valued Poincaré-Wirtinger inequality in 1D spatial domain, as well as a vectorvalued Agmon's inequality, it is shown that the suggested sampled-data fuzzy controller exponentially stabilizes the nonlinear DPSs in the sense of ∥·∥∞, if sufficient conditions presented in term of standard linear matrix inequalities (LMIs) are fulfilled. Moreover, an LMI relaxation technique is utilized to enhance exponential stabilization ability of the suggested sampled-data fuzzy controller. Finally, the satisfactory and better performance of the suggested sampled-data fuzzy controller are demonstrated by numerical simulation results of two examples.

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“…With the rapid development of communication technologies and digital information, some control strategies have attracted attention due to their simple maintenance, high efficiency, and low cost, for example, impulsive control, adaptive control, intermittent control, fuzzy control, sampled‐data control, and hybrid control . The sampled‐data controller is different from the continuous controller.…”

Section: Introductionmentioning

confidence: 99%

“…The sampled‐data control system has become an important issue in various research fields. Consequently, many scholars aim to study the stabilization of nonlinear dynamical systems via sampled‐data control . Impulsive control has been widely used in biological population control, electronic equipment design, pesticide spray dose supply, ecosystem control, and other fields .…”

Section: Introductionmentioning

confidence: 99%

Exponential stabilization for nonlinear coupled dynamical systems via impulsive and sampled‐data control with input constraints

Zhang

et al. 2019

Intl J Robust & Nonlinear

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Summary In this paper, exponential stabilization for nonlinear coupled dynamical systems by considering sampled‐data controller and impulsive controller with input constraints is investigated. Based on polytopic representation approach, some linear matrix inequalities are established to guarantee local exponential stabilization of nonlinear coupled dynamical systems. Moreover, by using polytopic differential inclusion, for the case of the partial input saturation involving in the impulsive controller, we also obtain several sufficient conditions ensuring local exponential stabilization. Finally, three examples are presented to show the effectiveness of theoretical analysis.

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Using exponential time-varying gains for sampled-data stabilization and estimation

Abstract: International audienc

Cited by 87 publications

References 14 publications

Delayed boundary control of a heat equation under discrete-time point measurements

Delayed boundary control of a heat equation under discrete-time point measurements

Spatially Piecewise Fuzzy Control Design for Sampled-Data Exponential Stabilization of Semilinear Parabolic PDE Systems

Exponential stabilization for nonlinear coupled dynamical systems via impulsive and sampled‐data control with input constraints

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