The synchronization criteria for uncertain nonlinear Caputo–Hadamard fractional-order systems with time-delay output feedback control

The methods of Master–Slave synchronization analysis with output feedback control for uncertain nonlinear Caputo-Hadamard fractional order systems without delay and with time-varying delay are presented in this study. To provide a synchronization criterion for the system instantaneously, we first apply the Lyapunov function approach for Caputo–Hadamard fractional order systems. Next, we construct novel synchronization conditions for the presence of time delay feedback control that ensure asymptotic stability of the error systems by combining fractional-order Halanay inequality with some features of the Caputo–Hadamard derivative. It is consequently possible to efficiently check the resulting conditions because they are provided in terms of linear matrix inequalities (LMIs). To demonstrate the usefulness of the acquired results, two numerical examples are suggested.