On the exponential stability of stochastic perturbed singular systems in mean square. (English) Zbl 1472.93152
Summary: 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.
MSC:
| 93D23 | Exponential stability |
| 93E15 | Stochastic stability in control theory |
| 93C70 | Time-scale analysis and singular perturbations in control/observation systems |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
Keywords:
stochastic perturbed singular systems; consistent initial conditions; Lyapunov techniques; Itô formula; Brownian motion; nontrivial solution; practical exponential stability in mean square; stabilizationReferences:
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