Robust D-Stability Testing Function for LTI Fractional Order Interval Systems

Abstract

This paper investigates the robust D-stability test of LTI fractional order interval systems (FOISes). The Dstability includes the performance of an LTI system in addition to stability. The coefficients of the system transfer function are uncertain parameters that each adopts a value in a real interval. Firstly, the concept of the value set is extended to the FOISes, and a necessary and sufficient condition is presented to study the robust D-stability of FOISes. Secondly, the value set of the FOISes is obtained analytically, and based on it a robust Dstability testing function is introduced to check the presented condition. The results obtained are applicable to systems of both commensurate and incommensurate orders. Finally, the theorems presented are applied to a space tether system.