Exponential Stability of Volterra Integro-Dynamic Sylvester Matrix System on Time Scales

This article investigates the exponential stability of the Volterra integro-dynamic (VID) Sylvester matrix system on time scales. The analysis begins by transforming the exponential stability VID Sylvester matrix system into an equivalent Kronecker product VID system using the vectorization operator. Subsequently, the boundedness properties of the solutions are rigorously established. Moreover, the theoretical results formulated on an arbitrary time scale unify and extend the stability conditions for both integral and discrete Volterra equations. Finally, the efficacy and validity of these findings are substantiated through diverse time scale scenarios, accompanied by a graphical comparative analysis.