Study on stability and stabilization of random impulsive differential Systems

Abstract

This thesis studies various stability results for random impulsive delay differential newlineequations, which is established the sufficient conditions for the exponential, weakly exponential, robust exponential, mean square exponential, mean square robust newlineexponential stability and exponential synchronization results of random impulsive newlinedifferential equations such as neutral type, finite and infinite delay, uncertain neutral newlinediscrete time-varying and distributed delay, uncertain singular time-delays. The newlineresults are obtained by using the method of maximum and minimum eigenvalues, newlineCauchy matrix, Lyapunov function, and Razumikhin technique. Moreover, the newlineexamples and graphical representations are shown consistency with theoretical newlinefindings as well as demonstrated the effectiveness of the random impulsive control newlineof the thesis. newline newline