Adaptive quantized controller design for synchronization of uncertain fractional-order nonlinear systems satisfying incremental quadratic constraints

This paper proposes the adaptive quantized controller design for the synchronization of a class of fractional-order nonlinear systems satisfying incremental quadratic constraints governed by an incremental multiplier matrix. The incremental quadratic constraints can describe many commonly encountered nonlinearities in existing literature. The adaptive quantized controller are designed and formulated in terms of matrix inequalities to make the error system asymptotically stable. Meanwhile, the sufficient conditions can be obtained via solving linear matrix inequalities. Moreover, an algorithm is presented to illustrate the steps of designing adaptive quantized controllers. Finally, examples about fractional-order Lorenz chaotic system and fractional-order Bloch system are provided to illustrate the effectiveness of the designed controller.