Multi-order Mittag-Leffler asymptotic synchronization of memory chaos in random initial-time non-autonomous nonlinear real order systems

Synchronization of memory chaos in zero initial-time real order systems has been vastly explored in the literature. Still, no results have been reported on random initial-time incommensurate version systems. We establish new local and global multi-order Mittag-Leffler asymptotic synchronization criteria under Lipschitz nonlinearity for random initial-time non-autonomous master–slave real order systems associated with different orders lying in the interval (0,1] via linear state feedback control. Some sufficient criteria deal with order-dependent and order-independent results that need the identification of a constant Metzler matrix and a non-negative matrix proposed to conclude multi-order Mittag-Leffler asymptotic synchronization between such systems. Synchronization demonstrations of real-order extensions of Wei and SMIB power systems illustrate the feasibility of the proposed approach and are practically convenient for new significance.