Abstract
Abstract For scalar quadratic optimal linear systems with a white gain coefficient, the influence of the uncertainty of the gain variance is analysed by means of elementary methods. First, the mean-square stability of the closed loop systems is analysed on the assumption that the controller is designed with an erroneous variance. It is shown that the use of an overestimated value of the variance less than a threshold value, which is infinite for the stable free systems, does not damage the stability of closed-loop systems. A relative underestimation error bound guaranteeing the stability of closed-loop systems is obtained. Secondly, performance of the controller designed with an erroneous variance is compared analytically with that of the certainty equivalence controller. An explicit relative overestimation error bound on the variance guaranteeing the superiority of the controller over the certainty equivalence controller is obtained.
Sign-in/Register to access full text options 
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.
