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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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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DOI: https://doi.org/10.1007/s11071-021-06620-y
Keywords
- Linear time-varying singular systems
- Standard canonical form
- Consistent initial conditions
- Lyapunov function
- Itô formula
- Brownian motion
- Nontrivial solution
- Practical exponential stability in mean square
- Stabilization