Finite-time stability of discrete autonomous systems

Haddad, Wassim M.; Lee, Junsoo

doi:10.1016/j.automatica.2020.109282

Cited by 65 publications

(9 citation statements)

References 14 publications

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“…holds true then, V (k + 1) − V (k) < 0 for all x k = 0 and consequently, system (14) is globally asymptotically stable. Remak that it is always possible to find α, β and γ to fulfill the convergence condition (19). In addition, the overall control feedback is only parameterized by one parameter α freely chosen between zero and one.…”

Section: Finite-time Stabilization Of Nonlinear Discrete-time Symentioning

confidence: 99%

“…Note that system (39) has been studied in [19] for the particular case where α = 1. For this particular case, the settling-time function was estimated by the integer k = ceil(|x 0 |/γ) for which the system trajectory is absolutely equal to zero for all k > k .…”

Section: Strong Finite-time Stabilization Of Nonlinear Discrete-tmentioning

confidence: 99%

“…For discrete-time systems, quite few investigations have been reported, see [16], [17], [18]. A Lyapunov characterization of finite-time stability of nonlinear autonomous systems is discussed in [19].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Finite-Time Stabilization Procedures for Discrete-Time Nonlinear Systems in Feedback Form

Ibrir

2021

IEEE Access

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New control procedures for finite-time stabilization of discrete-time nonlinear systems in strict-feedback form are proposed. The proposed designs enjoy the properties of being dependent on one design parameter and the ability to bring the whole state vector to the origin in finite time. Moreover, the settling-time functions are estimated in terms of the initial state vector and the unique design parameter that regulates the rate of the finite-time convergence. Finally, a trajectory-tracking control algorithm is presented and approved by numerical simulations. The simulation results have shown the excellent performance of the closed-loop system for different values of the free design parameter.

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Section: Finite-time Stabilization Of Nonlinear Discrete-time Symentioning

confidence: 99%

Section: Strong Finite-time Stabilization Of Nonlinear Discrete-tmentioning

confidence: 99%

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Finite-Time Stabilization Procedures for Discrete-Time Nonlinear Systems in Feedback Form

Ibrir

2021

IEEE Access

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“…From the late 19th century onwards, Lyapunov fundamental theorem [1] has been used by researchers to study asymptotic stability. Asymptotic stability means that a controlled system gradually converges to an equilibrium state over an unlimited amount of time [2]. However, in practical engineering, we prefer that the states of systems will reach equilibrium states in finite time.…”

Section: Introductionmentioning

confidence: 99%

Scaledp‐norm and its application in fast time‐synchronized control

Wang,

Su,

Chang

et al. 2023

IET Control Theory & Appl

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The definition of scaled p‐norm and its properties are given here. Compared with the norm‐normalized sign function, using scaled p‐norm in the controller design can not only achieve the time‐synchronized stability of non‐linear dynamic systems, but also improve the convergence rate of the system. Besides, the scaled p‐norm is applied to design the consensus protocol for multi‐agent systems, which enables the states of all agents to achieve fast time‐synchronized consensus. The simulation results demonstrate the superiority of this method in improving the convergence rate of the system.

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“…The most basic concepts of system stability include FTS [ 15 , 16 , 17 ] and Lyapunov asymptotic stability (LAS) [ 18 , 19 ]. FTS and LAS are different in two ways.…”

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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Finite-time stability of discrete autonomous systems

Cited by 65 publications

References 14 publications

Finite-Time Stabilization Procedures for Discrete-Time Nonlinear Systems in Feedback Form

Finite-Time Stabilization Procedures for Discrete-Time Nonlinear Systems in Feedback Form

Scaledp‐norm and its application in fast time‐synchronized control

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

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