Complex-Order Models: A System Identification Point of View

The present paper proposes a framework for the systematic and fruitful application of complex-order operators for modeling and control applications. We emphasize that special care must be taken when using complex-order elements to ensure that their responses to real-valued stimuli are real-valued themselves. The proposed complex-order real-valued elements enable the seamless generalization of their conventional real and integer-order counterparts. We further demonstrate how any linear operator can be extended in much the same way as the differintegral, by “raising” it to a power of a complex order, while ensuring that its kernel remains real-valued. The applicability of our considerations is demonstrated by a model of a compressed natural gas injection system.