General stability criteria for time-delay systems using a new delay-dependent reciprocally convex inequality

This study examines the improved stability conditions of a class of time-varying delay systems. It has been demonstrated that a novel reciprocally convex inequality (RCI) depends on its order (Formula presented.), providing a more generalized form of various existing RCIs. Consequently, by considering different values of (Formula presented.), different expressions for the lower bound of RCI can be obtained. Furthermore, by utilizing appropriate Lyapunov–Krasovskii functionals based on (Formula presented.), improved stability conditions have been achieved. After that, a new theorem has been presented, effectively addressing the shortcoming of existing stability conditions that have not been unified in a manner that covers the orders (Formula presented.) and 3. The study concludes with numerical examples that illustrate how the derived stability criteria, using the proposed generalized RCI, exhibit less conservatism compared to existing approaches.