Impulsive Functional Observer Design for Fractional-Order Nonlinear Systems Satisfying Incremental Quadratic Constraints

This paper considers the impulsive functional observer design problem for fractional-order nonlinear systems satisfying incremental quadratic constraints. The incremental quadratic constraints can describe many commonly encountered nonlinearities in the existing literature. Firstly, a fractional-order nonlinear system with incremental quadratic constraints and output nonlinearities is presented and the definition of incremental quadratic constraints is introduced. Secondly, an impulsive functional observer is designed to guarantee that the error system is exponentially stable. Thirdly, based on matrix partition, an approach to obtain the gains of the observer is proposed. Meanwhile, the sufficient conditions can be obtained via solving linear matrix inequalities. Subsequently, an algorithm is given to illustrate the steps of impulsive functional observer design. Finally, an example about fractional-order chaotic system is provided to illustrate the effectiveness of the designed controller.