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Uniform global asymptotic stability for nonlinear systems with delay and sampling

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Abstract

Nowadays, the time-delay and sampling of the control systems are considered as one of the most significant issues in the field of nonlinear control systems. It is undeniable that applying measurement delay with controls can cause the sampling of control laws with the delay in the behavior of nonlinear control systems. As a result, this paper introduces a new Lyapunov Krasovskii functional to prove the Uniformly Globally Asymptotic Stability (UGAS) for a class of continues nonlinear systems with the time delay and sampling. Hence, firstly, some assumptions are considered to simplify the complexity of the stability analysis of such systems. Secondly, the upper bounds of time-delays are obtained based on the suggested novel approach under a new theorem. Finally, an illustrative example is presented to show the effectiveness of our proposed method.

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Authors and Affiliations

  1. Department of Electronic and Electrical Engineering Department, Shiraz University of Technology, Shiraz, Iran

    Zeinab Echreshavi & Alireza Roosta

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  1. Zeinab Echreshavi
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  2. Alireza Roosta
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Correspondence to Zeinab Echreshavi.

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Appendix

Appendix

Inequality 1:

$${(a+b+c+d+e+f)^2} \leq 2{a^2}+2{b^2}+2{c^2}+2{d^2}+2{f^2}+4bc+4bd+4be+4bf+4cd+4ce+4cf+4de+4df$$

Jensen’s inequality:

$${\left| {\int \limits_{{{t_i} - \tau }}^{t} \psi \left( {m,{x_m}} \right)} \right|^2} \leq \left( {t - {t_i}+\tau } \right)\int \limits_{{{t_i} - \tau }}^{t} {\left| {\psi \left( {m,{x_m}} \right)} \right|^2}dm$$

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Echreshavi, Z., Roosta, A. Uniform global asymptotic stability for nonlinear systems with delay and sampling. Evolving Systems 10, 305–316 (2019). https://doi.org/10.1007/s12530-018-9239-7

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  • DOI: https://doi.org/10.1007/s12530-018-9239-7

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