Nullator's Stability Criterion for Linear, Time-Invariant Passive Networks

Abstract

In this paper a new method of determining stability of the linear, time-invariant, passive, portless RLC network is presented. The theory of this method is based on Lasalle theorem, an extension of Liapunov's stability theorem . In order to simplify a complicated network, and to apply the stability theorem, an ideal element, called nullator, is introduced. The nullator is a one-port network element defined by υ=0 and i =0, this means that it is simultaneously an open circuit and a short circuit. (In system theory , nullator may be defined as an ideal component with zero input and zero output for all time). Some theorems that can be used for testing stability of the network are developed, and they are in terms of network graphs. With these network graph theorems, some of the network can be easily checked by inspection. If the network is more complicated, the simplification rules developed by nullator can be applied, and then it will not be difficult to find all eigenvalues of the state equation written from the simplified network. The step- by -step testing procedures will be described in section 4.