Relative controllability of nonlinear fractional delay integrodifferential systems with multiple delays in control

Nirmala, R. Joice; Balachandran, K.

doi:10.14736/kyb-2017-1-0161

Cited by 3 publications

(3 citation statements)

References 31 publications

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“…In respect to linear delay differential control systems, we introduce the idea of a delayed control Grammian matrix and show how it correlates with the relative controllability of linear delayed control systems through its non‐singular property [34]. Similarly, in the process of assessing whether or not a nonlinear system with delays in state or control can be controlled, fixed point arguments are commonly used [8, 35–37]. Solutions to numerous problems in science and engineering are found by reducing them to an equivalent fixed‐point problem.…”

Section: Introductionmentioning

confidence: 99%

Results on relative controllability for nonlinear system with multi‐delays in control

Vinodkumar,

Hemalatha

2023

Math Methods in App Sciences

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This study uses a delayed matrix exponential to illustrate the solution of both linear and nonlinear delay problems using permutable matrices. We outline several prerequisites that are necessary to ensure the exponential stability of the trivial solution of delay systems. The conditions that are necessary and sufficient for the linear system to possess relative controllability are established by introducing a delayed Grammian matrix‐like criterion. A sufficient condition is obtained by Krasnoselskii's fixed point theorem for the relative controllability of nonlinear systems. Numerical examples provided at the end of the paper demonstrate the validity of our theoretical findings.

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Section: Introductionmentioning

confidence: 99%

Results on relative controllability for nonlinear system with multi‐delays in control

Vinodkumar,

Hemalatha

2023

Math Methods in App Sciences

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“…For uncertain nonlinear systems, [19] designs the robust finitetime sliding mode controller via a set of linear matrix inequalities (LMIs). It is noted that the time delay is not taken into account in most above works, which could degrade system performance and even cause system instability [20,21,22,23,24,25,26,27,28,29]. To cope with this, [30] addresses the problem of robust H ∞ SMC for uncertain neutraltype MJSs with time-varying delays.…”

Section: Introductionmentioning

confidence: 99%

<html>H<sub>∞</sub> sliding mode control for Markov jump systems with interval time-varying delays and general transition probabilities</html>

Li¹,

Zhang²,

Ou³

et al. 2019

Kybernetika

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“…However, so far, little attention reports on the relative controllability of fractional delay dynamical systems [12,13,14] but no relevant work has been reported on the higher oder dynamical systems. Inspired by this fact, the objective of this paper is to study the relative controllability of nonlinear higher order fractional delay integrodi¤erential equation with time varying delay in control via the Schaefer's …xed point theorem.…”

Section: Introductionmentioning

confidence: 99%

Relative controllability results for nonlinear higher order fractional delay integrodifferential systems with time varying delay in control

Sivabalan¹,

Sathiyanathan²

2018

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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This paper is concerned with the controllability of nonlinear higher order fractional delay integrodi¤erential equations with time varying delay in control, which involved Caputo derivatives of any di¤erent orders. A formula for the solution expression of the system is derived by using Laplace transform. A necessary and su¢ cient condition for the relative controllability of linear fractional delay dynamical systems with time varying delays in control is proved, and a su¢ cient condition for the corresponding nonlinear integrod-i¤erential equation has obtained. Examples has given to verify the results.

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Relative controllability of nonlinear fractional delay integrodifferential systems with multiple delays in control

Cited by 3 publications

References 31 publications

Results on relative controllability for nonlinear system with multi‐delays in control

Results on relative controllability for nonlinear system with multi‐delays in control

<html>H<sub>∞</sub> sliding mode control for Markov jump systems with interval time-varying delays and general transition probabilities</html>

Relative controllability results for nonlinear higher order fractional delay integrodifferential systems with time varying delay in control

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Relative controllability of nonlinear fractional delay integrodifferential systems with multiple delays in control

Cited by 3 publications

References 31 publications

Results on relative controllability for nonlinear system with multi‐delays in control

Results on relative controllability for nonlinear system with multi‐delays in control

<html>H<sub>&infin;</sub> sliding mode control for Markov jump systems with interval time-varying delays and general transition probabilities</html>

Relative controllability results for nonlinear higher order fractional delay integrodifferential systems with time varying delay in control

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<html>H<sub>∞</sub> sliding mode control for Markov jump systems with interval time-varying delays and general transition probabilities</html>