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On the Exponential Stability of Stochastic Perturbed Singular Systems in Mean Square

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Abstract

The approach of Lyapunov functions is one of the most efficient ones for the investigation of the stability of stochastic systems, in particular, of singular stochastic systems. The main objective of the paper is the analysis of the stability of stochastic perturbed singular systems by using Lyapunov techniques under the assumption that the initial conditions are consistent. The uniform exponential stability in mean square and the practical uniform exponential stability in mean square of solutions of stochastic perturbed singular systems based on Lyapunov techniques are investigated. Moreover, we study the problem of stability and stabilization of some classes of stochastic singular systems. Finally, an illustrative example is given to illustrate the effectiveness of the proposed results.

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Authors and Affiliations

  1. Universidad de Sevilla, Depto. Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Unversidad de Sevilla, c/ Tarfia s/n, 41012, Sevilla, 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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T. Caraballo: 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-I00, and by Junta de Andalucía (Consejería de Economía y Conocimiento) under Project US-1254251.

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Caraballo, T., Ezzine, F. & Hammami, M.A. On the Exponential Stability of Stochastic Perturbed Singular Systems in Mean Square. Appl Math Optim 84, 2923–2945 (2021). https://doi.org/10.1007/s00245-020-09734-8

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