Abstract
Abstract Since we have removed 0 + jO from the complex plane, the Nyquist map D × Ω (ℂ \ {0 + j0}, if it exists, could have a nontrivial homotopy class. The set of all possible homotopy classes of all such maps depends essentially on D. This chapter addresses the question as to what homotopy classes can be expected for a given uncertainty space. In case of such uncontractible uncertainty spaces as toris—multichannel phase margin problems—the set of all homotopy classes is quite large. The next question is to determine which of these homotopy classes yield closed-loop stability. Finally, given an uncertainty structure D, it is shown how the loop function L(s) induces a homotopy class of the map.
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.