LAUSR

The well-known generalized Kalman–Yakubovich–Popov lemma is widely used in system analysis and synthesis. However, the corresponding theory for singular systems, especially singular fractional-order systems (SFOSs), is lacking. Therefore, many control problems for this type of systems cannot be optimized in limited frequency ranges. In this article, a universal framework of the finite frequency band generalized Kalman–Yakubovich–Popov lemma for SFOSs is established, the bounded real lemma in the sense of the ${L_{\infty }}$ -norm is derived for different frequency ranges, and the corresponding controller is designed to improve the ${L_{\infty } }$ performance index of SFOSs. Three illustrative examples are given to demonstrate the correctness and effectiveness of the theoretical results.