Stability of discrete systems over a finite interval of time†

Abstract

In many cases of practical interest there is concern with the behaviour of dynamic systems only over a finite time interval. This concern may arise in one of two ways: In one case the system under consideration is defined over a fixed and finite interval of time, while in the second case the system in question is defined for all time; however, the behaviour of the system is of interest only over a finite time interval. Recently, Weiss and Infante (1965, 1967) treated the problem of system stability over a finite time interval for the ease of continuous systems. In this paper a theory is developed which concerns itself with the stability of discrete systems over a finite interval of time. The dynamic systems which are considered are general enough so as to include unforced systems, systems under the influence of perturbing forces, linear systems, non-linear systems, time invariant systems, time-varying systems, simple systems and composite systems. In the present development various definitions of stabilit...