Carathéodory Controllability Criterion for Nonlinear Dynamical Systems

[+] Author and Article Information
G. Langholz

Department of Electrical Engineering, School of Engineering, Tel-Aviv University, Tel-Aviv, Israel

M. Sokolov

Department of Fluid Mechanics and Heat Transfer, School of Engineering, Tel-Aviv University, Tel-Aviv, Israel

J. Dyn. Sys., Meas., Control 100(3), 209-213 (Sep 01, 1978) (5 pages) doi:10.1115/1.3426369 History: Received June 15, 1978; Online July 13, 2010


The question of whether a system is controllable or not is of prime importance in modern control theory and has been actively researched in recent years. While it is a solved problem for linear systems, it is still an open question when dealing with bilinear and nonlinear systems. In this paper, a controllability criterion is established based on a theorem by Carathéodory. By associating a given dynamical system with a certain Pfaffian equation, it is argued that the system is controllable (uncontrollable) if its associated Pfaffian form is nonintegrable (integrable).

Copyright © 1978 by ASME
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