Exponential Stability in Mean Square and Stochastic Variational Equations

2011 ◽  
Author(s):  
Adina Păucă ◽  
Diana Stoica ◽  
Ludovic Dan Lemle ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
...  
Keyword(s):  
Exponential Stability ◽  
Mean Square ◽  
Variational Equations ◽  
Stability In Mean Square

Existence and exponential stability for some stochastic neutral partial functional integrodifferential equations

2014 ◽  
Vol 22 (2) ◽  
Author(s):  
Mamadou Abdou Diop ◽  
Khalil Ezzinbi ◽  
Modou Lo
Keyword(s):  
Exponential Stability ◽  
Resolvent Operator ◽  
Mild Solutions ◽  
Linear Part ◽  
American Mathematical Society ◽  
Integrodifferential Equations ◽  
Mathematical Society ◽  
Mean Square ◽  
Nonlinear Part ◽  
Stability In Mean Square

Abstract.The aim of this work is to study the existence, uniqueness and exponential stability of mild solutions for some stochastic neutral partial functional integrodifferential equations. We suppose that the linear part has a resolvent operator in the sense given in Grimmer [Transactions of the American Mathematical Society 273 (1982), 333–349]. The nonlinear part is assumed to be continuous and lipschitzian with respect to the second argument. Firstly, we study the existence of mild solutions. Secondly we give some results on the exponential stability in mean square sense. An example is provided to illustrate the results of this work.

New stability criteria for stochastic perturbed singular systems in mean square

2021 ◽  
Author(s):  
Thomas Caraballo ◽  
Faten Ezzine ◽  
Mohamed ali Hammami
Keyword(s):  
Exponential Stability ◽  
Singular Systems ◽  
Time Varying ◽  
Mean Square ◽  
Stability Criteria ◽  
Uniform Exponential Stability ◽  
Lyapunov Techniques ◽  
Stability And Stabilization ◽  
Stochastic Singular Systems ◽  
Stability In Mean Square

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 con- ditions are consistent. Sucient 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 prob- lem of stability and stabilization of some classes of stochastic singular systems. Eventually, we provide a numerical example to validate the e ectiveness of the abstract results of this paper.

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