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 dynami c systems. The stability conditions are established by using the Lyapunov f unction 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 applicati ons of the established stability conditions, a class of retarded dynamic sy stems which have a linear retard-free term ave studied in detail and some e xponential, generalized exponential and non-exponential iterative decay est imates for the systems are obtained. It is shown that the non-exponential i terative decay estimates are less conservative than the exponential and gen eralized exponential decay estimates. In addition, the obtained iterative d ecay estimates involve only algebraic computation, therefore, they are simp le and very easy to use. Two examples are given to illustrate the proposed methods and to show the superiority of the obtained results.