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New stability criteria for stochastic perturbed singular systems in mean square

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Abstract

In this paper, we investigate the problem of stability of time-varying stochastic perturbed singular systems by using Lyapunov techniques under the assumption that the initial conditions are consistent. Sufficient conditions on uniform exponential stability and practical uniform exponential stability in mean square of solutions of stochastic perturbed singular systems are obtained based upon Lyapunov techniques. Furthermore, we study the problem of stability and stabilization of some classes of stochastic singular systems. Finally, we provide numerical examples to validate the effectiveness of the main results of this paper.

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Acknowledgements

The authors would like to thank the editor and the anonymous reviewer for valuable comments and suggestions, which allowed us to improve the paper.

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Authors and Affiliations

  1. Depto. Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, c/ Tarfia s/n, Sevilla, 41012, Spain

    Tomás Caraballo

  2. Faculty of Sciences of Sfax, Department of Mathematics, University of Sfax, Sfax, Tunisia

    Faten Ezzine & Mohamed Ali Hammami

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  1. Tomás Caraballo
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  2. Faten Ezzine
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  3. Mohamed Ali Hammami
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Correspondence to Mohamed Ali Hammami.

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The research of Tomás Caraballo has been partially supported by the Spanish Ministerio de Ciencia, Innovación y Universidades (MCIU), Agencia Estatal de Investigación (AEI) and Fondo Europeo de Desarrollo Regional (FEDER) under the project PGC2018-096540-B-I00, and by FEDER and Junta de Andalucía (Consejería de Economía y Conocimiento) under projects US-1254251, and P18-FR-4509.

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Caraballo, T., Ezzine, F. & Hammami, M.A. New stability criteria for stochastic perturbed singular systems in mean square. Nonlinear Dyn 105, 241–256 (2021). https://doi.org/10.1007/s11071-021-06620-y

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