Stability criteria for nonlinear Volterra integro-dynamic matrix Sylvester systems on measure chains

Abstract

Abstract In this paper, we establish sufficient conditions for various stability aspects of a nonlinear Volterra integro-dynamic matrix Sylvester system on time scales. We convert the nonlinear Volterra integro-dynamic matrix Sylvester system on time scale to an equivalent nonlinear Volterra integro-dynamic system on time scale using vectorization operator. Sufficient conditions are obtained to this system for stability, asymptotic stability, exponential stability, and strong stability. The obtained results include various stability aspects of the matrix Sylvester systems in continuous and discrete models.

Keywords

• Nonlinear Volterra integro-dynamic
• Stability
• Timescales