Abstract
This paper addresses the guaranteed cost control problem of a class of uncertain fractional-order (FO) delayed linear systems with norm-bounded time-varying parametric uncertainty. The study is focused on the design of state feedback controllers with delay such that the resulting closed-loop system is asymptotically stable and an adequate level of performance is also guaranteed. Stemming from the linear matrix inequality (LMI) approach and the FO Razumikhin theorem, a delay- and order-dependent design method is proposed with guaranteed closed-loop stability and cost for admissible uncertainties. Examples illustrate the effectiveness of the proposed method.
Highlights
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations
Successful applications in control, mathematics, mechanics, biology, chemistry, and signal and image processing [3,4,5,6,7,8,9,10] have shown that fractional calculus offers a new and deeper perspective in system modeling that overcomes the shortcomings of classical differential constitutive models [11,12]
The problem consists of the design of state-feedback controllers such that the resulting closed-loop system is robustly stable and a specified integral-quadratic cost function has an upper bound for all delays within the given intervals
Summary
A necessary and sufficient condition for testing the robust D-stability of linear time-invariant (LTI) general FO control systems was derived in [17]. Other studies regarding these topics can be found in [18,19,20] and references therein. To our best knowledge, we find limited results about the guaranteed cost control of FO uncertain delayed linear systems by using feedback controller with input delay. The problem consists of the design of state-feedback controllers such that the resulting closed-loop system is robustly stable and a specified integral-quadratic cost function has an upper bound for all delays within the given intervals.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
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
