RESEARCH PAPERS: Papers on Control Mechanics

Recursive Lyapunov Functions

[+] Author and Article Information
Andrzej Olas

Department of Mechanical Engineering, Oregon State University, Corvallis, Ore. 97331

J. Dyn. Sys., Meas., Control 111(4), 641-645 (Dec 01, 1989) (5 pages) doi:10.1115/1.3153107 History: Received March 04, 1988; Online July 21, 2009


The paper presents the concept of recursive Lyapunov function. The concept is applied to investigation of asymptotic stability problem of autonomous systems. The sequence of functions {Uα (i) } and corresponding performance measures λ(i) are introduced. It is proven that λ(i+1 ) ≤ λ(i) and in most cases the inequality is a strong one. This fact leads to a concept of a recursive Lyapunov function. For the very important applications case of exponential stability the procedure is effective under very weak conditions imposed on the function V = U(0) . The procedure may be particularly applicable for the systems dependent on parameters, when the Lyapunov function determined from one set of parameters may be employed at the first step of the procedure.

Copyright © 1989 by ASME
Topics: Stability
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