New stability criteria for stochastic perturbed singular systems in mean square

Caraballo, Tomás; Ezzine, Faten; Hammami, Mohamed Ali

doi:10.1007/s11071-021-06620-y

Cited by 11 publications

(7 citation statements)

References 26 publications

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“…Remark 3.1. Different authors handled the technique of structured perturbation for descriptor systems, see [1,11,12,17] for more details. Indeed, EΠg is a structured perturbation that guarantees "consistency" with the nominal descriptor system (2.1).…”

Section: Faten Ezzine Mohamed Ali Hammami and Walid Hdidimentioning

confidence: 99%

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Stability analysis of time–varying perturbed descriptor systems

Ezzine,

Hammami,

Hdidi

2024

JCD

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The manuscript deals with the analytical study of the "practical" stability of linear time dependent descriptor perturbed systems. The paper works out and proves the sufficient conditions (posed as LMIs) for practical stability of perturbed singular systems. The Gamidov's type integral inequality is used as a tool in the proof of the sufficient conditions of practical stability for perturbed singular systems. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach.

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Section: Faten Ezzine Mohamed Ali Hammami and Walid Hdidimentioning

confidence: 99%

“…Different authors investigate the problem of stability and stabilization of differential equations, see [19,21]. Recently, some sufficient conditions for the practical stability of descriptor systems have been reported in [11,12,17].…”

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confidence: 99%

Stability analysis of time–varying perturbed descriptor systems

Ezzine,

Hammami,

Hdidi

2024

JCD

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“…We will study the asymptotic behaviors of the solutions of the stochastic perturbed system (2.2) in the sense that all state trajectories are bounded and approach a sufficiently small neighborhood of the origin. In this objective, we recall the following definitions, see [10,11,12,13].…”

Section: Linear Time-invariant Stochastic Perturbed Systemsmentioning

confidence: 99%

“…Remark 2.1. Different authors tackle the problem of practical stability of stochastic differential equations via Lyapunov functions, see [10,11,12,13,14]. The construction of appropriate Lyapunov functions is not always possible, which motivates us to look for another method.…”

Section: Linear Time-invariant Stochastic Perturbed Systemsmentioning

confidence: 99%

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A new result on stabilization analysis for stochastic nonlinear affine systems via Gamidov’s inequality

Caraballo

Ezzine²,

Hammami³

2022

Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat.

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The Lyapunov approach is one of the most effective and efficient methods for the investigation of the stability of stochastic systems. Several authors analyzed the stability and stabilization of stochastic differential equations via Lyapunov techniques. Nevertheless, few results are concerned with the stability of stochastic systems based on the knowledge of the solution of the system explicitly. The originality of our work is to investigate the problem of stabilization of stochastic perturbed control-bilinear systems based on the explicit solution of the system by using the integral inequalities of the Gronwall type in particular Gamidov's inequality. Namely, under some restrictions on the perturbed term, and based on the method of integral inequalities, we prove that the stochastic system can be stabilized by constant feedback. Further, we study the problem of stabilization of stochastic perturbed control affine systems based on the use of bilinear approximation. Different examples are provided to verify the effectiveness of the proposed results.

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Estimates of Exponential Convergence for Solutions of Stochastic Nonlinear Systems

2023

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This paper aims to analyze the behavior of the solutions of a stochastic perturbed system with respect to the solutions of the stochastic unperturbed system. To prove our stability results, we have derived a new Gronwall-type inequality instead of the Lyapunov techniques, which makes it easy to apply in practice and it can be considered as a more general tool in some situations. On the one hand, we present sufficient conditions ensuring the global practical uniform exponential stability of SDEs based on Gronwall's inequalities. On the other hand, we investigate the global practical uniform exponential stability with respect to a part of the variables of the stochastic perturbed system by using generalized Gronwall's inequalities. It turns out that, the proposed approach gives a better result comparing with the use of a Lyapunov function. A numerical example is presented to illustrate the applicability of our results.

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New stability criteria for stochastic perturbed singular systems in mean square

Cited by 11 publications

References 26 publications

Stability analysis of time–varying perturbed descriptor systems

Stability analysis of time–varying perturbed descriptor systems

A new result on stabilization analysis for stochastic nonlinear affine systems via Gamidov’s inequality

Estimates of Exponential Convergence for Solutions of Stochastic Nonlinear Systems

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