Finite-time stability of linear fractional time-delay q-difference dynamical system

Ma, Kuikui; Sun, Shurong

doi:10.1007/s12190-017-1123-2

Cited by 11 publications

(7 citation statements)

References 19 publications

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“…1 depicts the state trajectories of the derive-response systems (4) and (7). The state trajectories of error system (11) under the order ξ = 0.6 are shown in Fig. 2.…”

Section: Examplesmentioning

confidence: 99%

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Novel algebraic criteria on global Mittag–Leffler synchronization for FOINNs with the Caputo derivative and delay

Yu-hong

Zhang

et al. 2021

J. Appl. Math. Comput.

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This paper focuses on the global Mittag-Leffler (M-L) synchronization for fractionalorder inertial neural networks (FOINNs) including the Caputo derivative and delay. By choosing an appropriate variable transformation, the considered system including the inertial term is transformed into two fractional-order nonlinearly coupled interconnected subsystems. Combining with the delayed-feedback controller, fractional Lyapunov functional approach and inequality analysis technique, multi sets of novel algebraic criteria on the global M-L synchronization between derive-response systems are established. The main prominent highlight of this paper is that the proposed results are characterized by the algebraic inequalities form, which can simplify the calculation and facilitate the test. Two numerical simulation examples validate the theoretical results.

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“…1 depicts the state trajectories of the derive-response systems (4) and (7). The state trajectories of error system (11) under the order ξ = 0.6 are shown in Fig. 2.…”

Section: Examplesmentioning

confidence: 99%

“…3 characterizes the state trajectories of systems ( 4) and (7) with the order ξ = 0.4. The state trajectories of error system (11) under the derivative orders ξ = 0.4 and ξ = 0.6 are presented in Figs. 4 and 5, respectively.…”

Section: Examplesmentioning

confidence: 99%

Novel algebraic criteria on global Mittag–Leffler synchronization for FOINNs with the Caputo derivative and delay

Yu-hong

Zhang

et al. 2021

J. Appl. Math. Comput.

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“…Remark From the proof of Theorem 1, we can see that the condition ( ν ( t )) α M < 1 is necessary to the theorem, which was ignored in previous works 6,8,13 …”

Section: A Generalized Fractional (Qh)–gronwall Inequalitymentioning

confidence: 98%

“…In 2020, Makhlouf et al 12 developed some Henry–Gronwall type q –fractional sum inequalities. However, for a nonnegative function x ( t ), the monotonicity of fractional sum function of x ( t ) is not specified in previous works, 6,8,13 which results in the incomplete proofs. In this paper, we adopt a new approach to avoid this problem.…”

Section: Introductionmentioning

confidence: 99%

A generalized fractional (q, h)–Gronwall inequality and its applications to nonlinear fractional delay (q, h)–difference systems

Jia

2021

Math Methods in App Sciences

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“…Fractional calculus is the subject of studying fractional integrals and fractional derivatives, which means that the orders of integration and differentiation are not integers. 1,2 During the last few decades, fractional calculus has evolved into an interesting and useful area of research in view of the extensive application of its modeling tools in applied and technical sciences. 3–5 Fractional-order differential systems are differential systems which involve fractional derivatives, and they have been successfully used to model many real-world phenomena such as electrical circuits, 6 fractional-order chaotic Lu 7 systems, and diffusion of heat through a semi-infinite solid where heat flow is equal to the half-derivative of the temperature, 8 quantum mechanics, 9 and fractional-order switched nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

State and disturbance simultaneous estimation for a class of nonlinear time-delay fractional-order systems

Huong

Yen

2021

Proceedings of the Institution of Mechanical Engineers, Part I:

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This article addresses the problem of estimating simultaneously the state and unknown disturbance of one-sided Lipschitz fractional-order systems with time-delay. The nominal models of nonlinearities are assumed to satisfy both the one-sided Lipschitz condition and the quadratically inner-bounded condition. Different from the state observer reported in the literature, which only dealt with one-sided Lipschitz integer-order time-delay systems or nonlinear fractional-order time-delay systems where the nonlinear function satisfying Lipschitz condition, the state observers in this article can be applied to a wide class of nonlinear time-delay systems (one-sided Lipschitz fractional-order time-delay systems and one-sided Lipschitz integer-order time-delay systems). We employ the Razumikhin stability theorem and a recent result on the Caputo fractional derivative of a quadratic function to derive a sufficient condition for the asymptotic stability of the observer error dynamic system. The stability condition is obtained in terms of linear matrix inequalities, which can be effectively solved using the MATLAB LMI Control Toolbox. Two examples are provided to show the effectiveness of the proposed design approach.

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Finite-time stability of linear fractional time-delay q-difference dynamical system

Cited by 11 publications

References 19 publications

Novel algebraic criteria on global Mittag–Leffler synchronization for FOINNs with the Caputo derivative and delay

Novel algebraic criteria on global Mittag–Leffler synchronization for FOINNs with the Caputo derivative and delay

A generalized fractional (q, h)–Gronwall inequality and its applications to nonlinear fractional delay (q, h)–difference systems

State and disturbance simultaneous estimation for a class of nonlinear time-delay fractional-order systems

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