Order-distributions and the Laplace-domain logarithmic operator

Advances in Difference Equations

Tom T. Hartley¹  Carl F. Lorenzo² 

[1] Department of Electrical and Computer Engineering, University of Akron, Akron, USA;NASA Glenn Research Center, Cleveland, USA

关键词: Order-distribution;    Laplace transform;    Fractional-order systems;    Fractional calculus;   

DOI  :  10.1186/1687-1847-2011-59

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

This paper develops and exposes the strong relationships that exist between time-domain order-distributions and the Laplace-domain logarithmic operator. The paper presents the fundamental theory of the Laplace-domain logarithmic operator, and related operators. It is motivated by the appearance of logarithmic operators in a variety of fractional-order systems and order-distributions. Included is the development of a system theory for Laplace-domain logarithmic operator systems which includes time-domain representations, frequency domain representations, frequency response analysis, time response analysis, and stability theory. Approximation methods are included.

【 授权许可】

CC BY