Stability of large-scale hereditary systems with infinite retardations

Abstract

In this paper, a general theory for large-scale functional differential systems with finite and infinite retardations is developed by employing the theory of systems of functional differential inequalities. The functional differential inequality for the subsystem with infinite retardation is developed following the results of Coleman and Mizel (1968). Finally, a comparison theorem in the framework of vector Lyapunov function has been employed to investigate the stability of hereditary interconnected systerna. An example to illustrate the results is given.