On the Evaluation of Quadratic Cost Functionals for Linear Feedback Fractional-Order Systems

C. Hwang and Y.-C. Cheng (Taiwan)


Quadratic cost functionals, Integral squared error, Fractional-order systems, Product-to-sum decomposition, branch cut


In the literature the concept of product-to-sum decompo sition E(s)E(−s) = F (s) + F (−s), where E(s) is a Hurwitz stable transfer function, has been extensively ap plied to derive parametric expressions for quadratic cost functionals of linear time-invariant systems, including a class of commensurate pure delay and distributed delay systems. We show in this paper that due to the multival uedness of the transfer function and the existence of non removable branch-cut singularity, the extension of such a concept to obtain closed-form expression for the integral squared-error of fractional-order systems is generally not possible. Hence, the calculation of the quadratic function als of fractional-order systems has to resort a numerical in tegration scheme. In this aspect, a reliable and efficient nu merical approach based on solving a differential equation is suggested for obtaining accurate solutions.

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