A Trace Method for Directly Synthesizing Liapunov Functions of Aperiodic Systems

[+] Author and Article Information
C. F. Chen, L. S. Shieh

University of Houston, Houston, Texas

J. Basic Eng 92(2), 398-400 (Jun 01, 1970) (3 pages) doi:10.1115/1.3425008 History: Received December 23, 1969; Online October 27, 2010


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.

Copyright © 1970 by ASME
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