The Extended Strictly Positive Real Lemma for Fractional Order Systems with Distributed Delay and Application to Robust Control

This article delves into the intricate world of fractional order systems, highlighting their superior ability to model complex engineering behaviors due to their hereditary and memory effects. It introduces an extended strictly positive real lemma tailored for fractional order systems with distributed delay, a critical aspect often overlooked in existing literature. The manuscript tackles the challenges posed by order and delay information loss, as well as the complexities of bilinear matrix inequalities in robust control analysis. It presents groundbreaking results, including an order-dependent and delay-dependent lemma for nominal systems and a robust control condition for uncertain systems, all formulated as linear matrix inequalities for ease of calculation and application. Through rigorous proofs and illuminating numerical examples, the article demonstrates the effectiveness of the proposed approaches, paving the way for enhanced system stability and performance under external disturbances and parameter variations.