Mittag-Leffler asymptotic stabilization of random initial-time nonlinear real-order control systems

In many real-order nonlinear systems, measuring the control performance decay of states seems quite puzzling and difficult via the implementation of different control strategies. We introduce Mittag-Leffler asymptotic stabilization to random initial-time nonlinear real-order systems defined in the sense of Caputo derivative by implementing a new linear affine state feedback control law. Using the Caputo derivative quadratic inequality and comparison method, two new theorems deal with order-dependent and order-independent results to conclude local and global Mittag-Leffler asymptotic stabilization under Lipschitz nonlinearity are forward. Some sufficient criteria to develop simplified results for Mittag-Leffler asymptotic stabilization are presented. We illustrate the applicability of our results by giving two examples.