Stability-Boundary Approximations for Relay-Control Systems Via a Steepest-Ascent Construction of Lyapunov Functions

[+] Author and Article Information
S. Weissenberger

Department of Mechanical Engineering, University of Santa Clara, Santa Clara, Calif.

J. Basic Eng 88(2), 419-428 (Jun 01, 1966) (10 pages) doi:10.1115/1.3645874 History: Received July 26, 1965; Online November 03, 2011


This paper presents a new technique for constructing Lyapunov functions for estimating the domain of asymptotic stability of nonlinear control systems. A machine program assigns figures of merit (based on the quality of the stability-boundary estimates) to the members of a set of Lyapunov functions and then searches for the one which maximizes this measure. The method is applied to relay-control systems, which are not tractable by other systematic techniques such as the method of Zubov. The paper is divided into two parts. The first part contains a discussion of the motions of relay-control systems and the technique of investigating their stability domains with Lyapunov functions. The second part contains a discussion of existing methods of generating Lyapunov functions and a description of the new method, along with a number of second and third-order examples.

Copyright © 1966 by ASME
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