Abstract
Following Douglas's ideas on the inverse problem of the calculus of variations, the purpose of this article is to show that one can use formal integrability theory to develop a theory of elimination for systems of partial differential equations and apply it to control theory. In particular, we consider linear systems of partial differential equations with variable coefficients and we show that we can organize the integrability conditions on the coefficients to build an “intrinsic tree”. Trees of integrability conditions naturally appear when we test the structural properties of linear multidimensional control systems with some variable or unknown coefficients (controllability, observability, invertibility, …) or for generic linearization of nonlinear systems.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.