Abstract
In this paper we give a new proof that for controllable and observable linear systems every L 2 [ 0 , T ] function can be approximated in the L 2 [ 0 , T ] sense with an output function generated by an L 2 [ 0 , T ] input function. We also give a new characterization of how continuous functions on [ 0 , T ] are uniformly approximated by an output generated by a continuous input function. The relative degree of the transfer function of the system determines those functions that can be approximated. We further show that if the initial data is allowed to vary then every continuous function is uniformly approximated by outputs generated by continuous functions.
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.
