On the Practical h-stability of Nonlinear Systems of Differential Equations

Ghanmi, Boulbaba

doi:10.1007/s10883-019-09454-5

Cited by 13 publications

(8 citation statements)

References 17 publications

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“…Next, a precise definition of the practical uniform h -stability is given as follows which will be used in subsequent main results (see for instance Damak et al , 2020a, 2020b; Ghanmi, 2019).…”

Section: Mathematical Preliminariesmentioning

confidence: 99%

“…Moreover, the authors in Damak et al (2021) gave sufficient conditions to ensure the global uniform h -stability of control systems under a continuous linear controller. Lyapunov’s function method is efficiently used for solving questions about practical stability in many problems of applied mathematics for system analysis and control design (Ghanmi, 2019). The investigation of practical stabilization for nonlinear systems has been widely studied for many years (Benabdallah and Hammami, 2008; Damak et al , 2013; Ellouze and Hammami, 2007; Hammami, 2001; Soldatos and Corless, 1991).…”

Section: Introductionmentioning

confidence: 99%

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On the practical h-stabilization of nonlinear time-varying systems: application to separately excited DC motor

Damak

Hammami

Kicha

2021

COMPEL

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Purpose The purpose of this paper is to report on the global practical uniform h-stabilization for certain classes of nonlinear time-varying systems and its application in a separately excited DC motor circuit. Design/methodology/approach Based on Lyapunov theory, the practical h-stabilization result is derived to guarantee practical h-stability and applicated in a separately excited DC motor. Findings A controller is designed and added to the nonlinear time-varying system. The practical h-stability of the nonlinear control systems is guaranteed by applying the appropriate controller based on Lyapunov second method. Another effective controller is also designed for the global practical uniform h-stability on the separately excited DC motor with load. Numerical simulations are demonstrated to verify the effectiveness of the proposed controller scheme. Originality/value The introduced approach is interesting for practical h-stabilization of nonlinear time-varying systems and its application in a separately excited DC motor. The original results generalize well-known fundamental result: practical exponential stabilization for nonlinear time-varying systems.

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Section: Mathematical Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the practical h-stabilization of nonlinear time-varying systems: application to separately excited DC motor

Damak

Hammami

Kicha

2021

COMPEL

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“…In 2016, Stamova [20] derived the practical stability criteria of fractional-order impulsive control systems by using fractional comparison principle, scalar and vector Lyapunovlike functions. In 2017, Agarwal [2] investigated practical stability of nonlinear fractional differential equations with noninstantaneous impulses and presented a new definition of the derivative of a Lyapunov-like function; see literatures [2,3,9,11,20] for more details.…”

Section: Introductionmentioning

confidence: 99%

Practical stability for fractional impulsive control systems with noninstantaneous impulses on networks

You

Sun

2022

NAMC

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This paper investigates practical stability for a class of fractional-order impulsive control coupled systems with noninstantaneous impulses on networks. Using graph theory and Lyapunov method, new criteria for practical stability, uniform practical stability as well as practical asymptotic stability are established. In this paper, we extend graph theory to fractional-order system via piecewise Lyapunov-like functions in each vertex system to construct global Lyapunov-like functions. Our results are generalization of some known results of practical stability in the literature and provide a new method of impulsive control law for impulsive control systems with noninstantaneous impulses. Examples are given to illustrate the effectiveness of our results

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“…The analysis of practical stability for nonlinear systems has become one of the important research topics in the field of control theory and its applications. Recent years, this subject has achieved a number of excellent research results, see References 20‐24 for delay free systems, and References 25‐31 for time‐delay systems. Stamova 27 used the vector Lyapunov function method and the differential inequalities of piecewise continuous functions to study the practical stability of solutions of impulsive nonlinear functional differential equations.…”

Section: Introductionmentioning

confidence: 99%

Lyapunov matrix‐based method to global robust practical exponential r‐stability for a class of delayed continuous‐time nonlinear systems: Theory and applications

Yang

Wang

Zhang

et al. 2022

Intl J Robust & Nonlinear

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This article involves the problem of global robust practical exponential r-stability for a class of delayed continuous-time nonlinear systems. By proposing a method based on Lyapunov matrix, a global robust practical exponential r-stability criterion of the considered systems is established. The criteria are expressed as uncomplicated linear matrix inequalities. Therefore, standard calculation software can be used for verification. In addition, the proposed method is applied to the practical stabilization problem of three-state turbocharged diesel engine model, and a good control effect is obtained.

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On the Practical h-stability of Nonlinear Systems of Differential Equations

Cited by 13 publications

References 17 publications

On the practical h-stabilization of nonlinear time-varying systems: application to separately excited DC motor

On the practical h-stabilization of nonlinear time-varying systems: application to separately excited DC motor

Practical stability for fractional impulsive control systems with noninstantaneous impulses on networks

Lyapunov matrix‐based method to global robust practical exponential r‐stability for a class of delayed continuous‐time nonlinear systems: Theory and applications

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