Stability and Stabilization of Nonlinear Time-Delay Systems Using Conformable Derivatives with One-Sided Lipschitz Nonlinearities and Quadratic Inner-Boundedness Constraints

This paper investigates the stability analysis and stabilization problems for a class of nonlinear time-delay systems described by conformable derivatives. We consider systems with one-sided Lipschitz nonlinearities and quadratic inner-boundedness conditions, which encompass a broad range of practical applications. Through the construction of appropriate Lyapunov-Krasovskii functionals, we develop novel linear matrix inequality (LMI) conditions for exponential stability of autonomous systems and practical exponential stability for systems subject to bounded perturbations. Furthermore, we propose state-feedback stabilization strategies that transform the controller design problem into a convex optimization framework solvable via efficient LMI techniques. The theoretical developments are comprehensively validated through numerical examples that demonstrate the effectiveness of the proposed stability and stabilization criteria. The results establish a rigorous framework for analyzing and controlling conformable fractional-order systems with time delays, bridging theoretical advances with practical implementation considerations.