Abstract

This paper deals with the standard periodic Riccati differential equation. A complete necessary and sufficient condition is presented for the existence of Hermitian periodic positive definite (HPPD) solution. Previously, after a proper change of basis in the state space the condition can be expressed in terms of the notions of stabilizability and detectability. Moreover, it is shown that when a HPPD solution exists, it is either unique, or else there are uncountably many such solutions. The result of the paper can be considered as a valid extension of Richardson and Kwong's (1986) result to the periodic version.

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 call

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.