A Trace Method for Directly Synthesizing Liapunov Functions of Aperiodic Systems

Abstract

A direct synthesis technique is established for constructing the Liapunov function of a completely aperiodic system without assuming elements and solving simultaneous equations. By inspecting the traces of the state matrix and its products, a Liapunov function and its derivative can be immediately written. The determinant which has the same elements of the Liapunov function so obtained turns out to be a new criterion for testing whether or not a system involves repeated roots. This determinant for an aperiodic system is closely analogous to the Hurwitz determinant for a stable system.