Guaranteed cost control of delayed conformable fractional-order systems with nonlinear perturbations using an event-triggered mechanism approach

The study of conformable fractional-order systems has gained significant importance due to their ability to model complex dynamic behaviors across various applications. However, these systems encounter several challenges, such as the unique properties of conformable derivatives, the presence of nonlinear perturbations, and time-varying delays, all of which complicate stability and control design. Additionally, traditional control approaches often struggle to balance stability, performance, and efficient resource utilization, particularly when addressing event-triggered mechanism that are prone to Zeno behavior. This paper tackles these challenges by proposing a novel event-triggered control framework to solve the guaranteed cost control problem for delayed conformable fractional-order systems with nonlinear perturbations. By utilizing the Razumikhin stability theorem and conformable fractional calculus, we derive sufficient conditions in the form of linear matrix inequalities (LMIs) for the existence of guaranteed cost state-feedback control. A key contribution of this work is the development of a criterion to eliminate Zeno behavior, ensuring the practical implementation of the event-triggered control strategy. The feasibility and effectiveness of the proposed approach are demonstrated through two simulation examples: a conformable fractional-order neural network and an electrical circuit model.