Decay estimates for retarded dynamic systems

This paper presents some necessary and sufficient stability conditions and some sufficient stability conditions for general classes of retarded dynamic systems. The stability conditions are established by using the Lyapunov function method. However, attention is paid in this paper to establishing as less conservative exponential, generalized exponential and non-exponential decay estimates for the retarded dynamic systems as possible. As applications of the established stability conditions, a class of retarded dynamic systems which have a linear retard-free term are studied in detail and some exponential, generalized exponential and non-exponential iterative decay estimates for the systems are obtained. It is shown that the non-exponential iterative decay estimates are less conservative than the exponential and generalized exponential decay estimates. In addition, the obtained iterative decay estimates involve only algebraic computation; therefore, they are simple and very easy to use. Two examples are giv...