Stability of a class of interconnected systems†

Abstract

Sufficient conditions are given for exponential stability of the equilibrium of systems of interconnected components taken from a class of nonlinear, time-varying, multi-terminal, differential, algebraic and mixed components. The analysis is based on the mathematical models of the unconstrained components and the linear constraints imposed by the interconnections between the components. A Liapunov function is constructed for the interconnected system from Liapunov functions for the individual components. A parameter vector appearing in the Liapunov function is selected in a prescribed optimal manner. The Liapunov function so constructed can be used to establish a lower bound on the rate of decay of the system. An example of a ninth-order, non-linear system is included to demonstrate the application to design.