Abstract
We introduce and study collinearity as a systems theoretic property, asking whether coupled dynamical systems with collinear initial conditions maintain collinear solutions for all times. Completely characterizing such collinear dynamical systems, we find that they define a Lie algebra whose Lie group are the invertible collinearity-preserving maps. Our characterization of collinear systems then allows us to determine state feedbacks which enforce collinear solutions in coupled control systems. Further, we characterize coupled linear differential equations whose solutions will asymptotically become collinear. Last, we characterize collinearity of multiple dynamical systems and their ability to produce coplanar solutions. Our findings relate to flows on the real projective spaces and Grassmannians.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
