Stability, transient behaviour and trajectory bounds of interconnected systems†

Publisher Website
Google Scholar
Abstract
In practice, many systems are complex and of high dimension. Many such systems may be viewed as being composed of several simpler sub-systems which when connected in an appropriate fashion yield the original composite system. The stability, the transient behaviour and estimates for the trajectory bounds of certain composite systems are analysed in terms of their sub-systems. This is accomplished by defining the stability of sub-systems and of composite systems in terms of certain time-varying sub-sets of the state space which are pre-specified in a given problem. After stating definitions of stability for sub-systems which are under the influence of perturbing forces and for composite systems, theorems are stated and proved which yield sufficient conditions for stability. These theorems involve the existence of Lyapunov-like functions which do not possess any particular definiteness requirements on V and [Vdot]. The time-varying sub-sets of the state space which are utilized in the stability definitions and which arise in conjunction with the stability theorems yield estimates of the transient behaviour and of the trajectory bounds of both sub-systems and composite systems. To demonstrate the generality of the developed theory, several special cases are considered. Also, some specific examples are worked out to demonstrate the methods involved.

This publication has 4 references indexed in Scilit: