Technical Reports (ESE)


The “mechanical systems” define a large and important class of highly nonlinear dynamical equations which, for example, encompasses all robots. In this report it is shown that a strict Lyapunov Function suggested by the simplest examplar of the class - a one degree of freedom linear time invariant dynamical system - may be generalized over the entire class. The report lists a number of standard but useful consequences of this discovery. The analysis suggests that the input-output properties of the entire class of nonlinear systems share many characteristics in common with those of a second order, phase canonical, linear time invariant differential equation.

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Technical Report

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NOTE: At the time of publication, author Daniel Koditschek was affiliated with Yale University. Currently, he is a faculty member in the Department of Electrical and Systems Engineering at the University of Pennsylvania.

Bib Tex

@inproceedings{kod-yale-1987-1, title = {Quadratic Lyapunov Functions for Mechanical Systems.}, author = {D.E. Koditschek}, booktitle = {Center for Systems Science, Yale University}, year = {1987}, month = {March}, }



Date Posted: 02 October 2017

This document has been peer reviewed.