Finite-Time Control for Nonlinear Systems with Time-Varying Delay and Exogenous Disturbance

Ruan, Yanli; Huang, Tianmin

doi:10.3390/sym12030447

Cited by 8 publications

(4 citation statements)

References 36 publications

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“…Maintaining the stability of solutions in contemporary nonlinear dynamical systems has been a major challenge in their operation [1][2][3][4]. Conventionally [5][6][7][8][9][10][11][12][13][14][15][16][17], Lyapunov's second method is used to study the stability and optimization of solutions in systems composed of ordinary differential equations. For instance, in [5], Lyapunov's stability theory is employed to establish the global asymptotic stability of the periodic solution in a recognized ecosystem model.…”

Section: Introductionmentioning

confidence: 99%

A Method of Qualitative Analysis for Determining Monotonic Stability Regions of Particular Solutions of Differential Equations of Dynamic Systems

Lyubimov

2023

Mathematics

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Developing stability analysis methods for modern dynamical system solutions has been a significant challenge in the field. This study aims to formulate a qualitative analysis approach for the monotone stability region of a specific solution to a single differential equation within a dynamical system. The system in question comprises two first-order nonlinear ordinary differential equations of a particular kind. The method proposed hinges on applying elements of combinatorics to the traditional mathematical investigation of a function with a single independent variable. This approach enables the exact determination of the different qualitative scenarios in which the desired solution changes, under the assumption that the function values monotonically diminish from a specified value down to a finite zero. This paper outlines the creation and decomposition of the monotone stability region associated with the solution under consideration.

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Section: Introductionmentioning

confidence: 99%

A Method of Qualitative Analysis for Determining Monotonic Stability Regions of Particular Solutions of Differential Equations of Dynamic Systems

Lyubimov

2023

Mathematics

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“…The authors of [ 11 ] developed robust stability of switching systems with nonlinear disturbances and interval TVD. Finite-time control problems for nonlinear systems with TVD and external interference were discussed in [ 12 ]. In general, there is often uncertainty in the parameters of the system model.…”

Section: Introductionmentioning

confidence: 99%

Robust Finite-Time Stability for Uncertain Discrete-Time Stochastic Nonlinear Systems with Time-Varying Delay

Liu

Wang

et al. 2022

Entropy

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The main concern of this paper is finite-time stability (FTS) for uncertain discrete-time stochastic nonlinear systems (DSNSs) with time-varying delay (TVD) and multiplicative noise. First, a Lyapunov–Krasovskii function (LKF) is constructed, using the forward difference, and less conservative stability criteria are obtained. By solving a series of linear matrix inequalities (LMIs), some sufficient conditions for FTS of the stochastic system are found. Moreover, FTS is presented for a stochastic nominal system. Lastly, the validity and improvement of the proposed methods are shown with two simulation examples.

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“…Because states of the system depend on the present time and a time period in the past, time delays occur in dynamical systems, and ignoring their effect yields severe deterioration in system performance or even system instability [5,6]. Thus, control of time-delay systems is known to have practical significance [7][8][9]. Recent decades have observed a widespread attention given to the synthesis of appropriate control laws for time-delay dynamical systems in the presence of parameter uncertainties [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

An LMI Approach to Nonlinear State-Feedback Stability of Uncertain Time-Delay Systems in the Presence of Lipschitzian Nonlinearities

et al. 2020

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This article proposes a new nonlinear state-feedback stability controller utilizing linear matrix inequality (LMI) for time-delay nonlinear systems in the presence of Lipschitz nonlinearities and subject to parametric uncertainties. Following the Lyapunov–Krasovskii stabilization scheme, the asymptotic stability criterion resulted in the LMI form and the nonlinear state-feedback control technique was determined. Due to their significant contributions to the system stability, time delays and system uncertainties were taken into account while the suggested scheme was designed so that the system’s stabilization was satisfied in spite of time delays and system uncertainties. The benefit of the proposed method is that not only is the control scheme independent of the system order, but it is also fairly simple. Hence, there is no complexity in using the proposed technique. Finally, to justify the proficiency and performance of the suggested technique, a numerical system and a rotational inverted pendulum were studied. Numerical simulations and experimental achievements prove the efficiency of the suggested control technique.

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Finite-Time Control for Nonlinear Systems with Time-Varying Delay and Exogenous Disturbance

Cited by 8 publications

References 36 publications

A Method of Qualitative Analysis for Determining Monotonic Stability Regions of Particular Solutions of Differential Equations of Dynamic Systems

A Method of Qualitative Analysis for Determining Monotonic Stability Regions of Particular Solutions of Differential Equations of Dynamic Systems

Robust Finite-Time Stability for Uncertain Discrete-Time Stochastic Nonlinear Systems with Time-Varying Delay

An LMI Approach to Nonlinear State-Feedback Stability of Uncertain Time-Delay Systems in the Presence of Lipschitzian Nonlinearities

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