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.
Highlights
Differential-algebraic equations (DAEs) are a combination of differential equations along with algebraic constraints
We obtain a generalization of differential-algebraic equations (DAEs) and stochastic differential equations (SDEs)
We consider the combination of Ito stochastic representation and linear timevarying singular form to consider a large class of realistic systems that are modeled with stochastic differential-algebraic equations (SDAEs)
Summary
Differential-algebraic equations (DAEs) are a combination of differential equations along with algebraic constraints. We consider the combination of Ito stochastic representation and linear timevarying singular form to consider a large class of realistic systems that are modeled with stochastic differential-algebraic equations (SDAEs). To the best of our knowledge, no work has been published about the practical stability of linear time-varying stochastic perturbed singular systems. Based upon the method of Lyapunov functions and generalized Gronwall inequalities, we establish some criteria for uniform exponential stability and practical uniform exponential stability in mean square of a class of linear time-varying stochastic perturbed systems.
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