Analysis of discontinuous large-scale systems: stability, transient behaviour and trajectory bounds

Abstract

The trajectory bounds of simple and large-scale interconnected discontinuous systems are treated within a stability framework. In doing so, stability is defined in terms of pre-specified subsets of the state space over an infinite time interval (practical stability) and over a finite time interval (finite time stability). The discontinuous systems considered are those which are described by ordinary discontinuous differential equations which may be autonomous or non-autonomous, linear or non-linear, unforced or under the influence of persistent disturbances, simple or interconnected. In all cases it is assumed that the differential equation possesses solutions in the sense of Filippov. The results obtained yield sufficient conditions for practical and finite time stability. The interconnected systems are treated in terms of their subsystems. In order to demonstrate the methods involved, some examples are considered.