On the decay rate of solutions of non-autonomous differential systems

Abstract

Some results on the asymptotic behaviour of solutions of differential equations concerning general decay rate are proved. We prove general criteria on the exponential, polynomial, and more general decay properties of solutions by using suitable Lyapunov's functions. We also present a detailed analysis of the perturbed linear and nonlinear differential systems. The theory is illustrated with several examples.

Keywords

• Asymptotic behaviour
• exponential and polynomial stability
• rate of decay.