New <i>ψ</i> ‐Mittag‐Leffler Asymptotic Stability and Stabilization of Nonlinear <i>ψ</i> ‐Caputo Fractional Systems

ABSTRACT In many applications of interest, the dynamics of systems described by universal differential operators are widely known. Is it possible to control the non‐asymptotic or unstable dynamics of such‐type systems? We consider nonlinear ‐Caputo fractional order systems and design a linear state feedback control technique to address a novel concept, ‐Mittag‐Leffler asymptotic stabilization. By using a quadratic positive function and Lyapunov function inequality, we establish local and global conditions for ‐Mittag‐Leffler asymptotic stability and stabilization under Lipschitz perturbation and a norm bound nonlinearity. The interesting aspects of our proposed results have been applied to five non‐trivial systems to show the intuitive understanding of systems. We discover that two systems give rise to memory chaos, whereas it is shown that under the action of an implemented linear state feedback controller, it can be possible to control the memory chaotic dynamics to some control objective.