A Converse Theorem on Practical h-Stability of Nonlinear Systems

Damak, Hanen; Hammami, Mohamed Ali; Kicha, A.

doi:10.1007/s00009-020-01518-2

Cited by 13 publications

(8 citation statements)

References 16 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%

“…In particular, Definition 4 generalizes the notion of h-stability where r = 0. Moreover, the practical h-stability property (2) includes the concepts of practical exponential stability when h ( t ) = e –λt , with λ > 0 (Benabdallah et al , 2009) and practical polynomial stability when h(t)=1(1+t)γ, with γ > 0, (Damak et al , 2020a).…”

Section: Mathematical Preliminariesmentioning

confidence: 99%

“…In this work, we concern with practical problems, especially problems from the area of controls, such a concept called practical h -stability. In Damak et al (2020a, 2020b), the authors studied the convergence of trajectories of certain nonlinear systems in the practical h -stability case. 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.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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: Mathematical Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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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“…Because of that, the concept of h-stability is very useful and more general in the study of differential systems. This theory has been developed very intensively and several works are published, see [4][5][6]. However, when the origin is not necessarily an equilibrium point, the desired system may be unstable and yet the system may oscillate sufficiently near this state so that its performance is acceptable and still possible to analyze the asymptotic of solutions with respect to a small neighborhood of the origin, which yields to the concept of practical stability, see [1,2,10].…”

Section: Introductionmentioning

confidence: 99%

h-stability and boundedness results for solutions to certain nonlinear perturbed systems

Damak¹,

Hammani²,

Kicha³

2021

Math. Appl.

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In this work, we establish some new sufficient conditions to show the uniform h-stability for nonlinear time-varying perturbed systems which can be viewed as an extension of the uniform exponential stability and polynomial stability. Also, we study the boundedness of solutions when the origin is not necessarily an equilibrium point of the perturbed system. The idea is to use some Gronwall type integral inequalities. As an illustration, we present some examples with simulations to show the applicability of the obtained results.

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A Converse Theorem on Practical h-Stability of Nonlinear Systems

Cited by 13 publications

References 16 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

h-stability and boundedness results for solutions to certain nonlinear perturbed systems

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