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

This paper investigates the robust D-stability test of LTI fractional order interval systems (FOISes). The D-stability 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 D-stability 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.