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 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.

[1]  Mehmet Önder Efe,et al.  Neural Network Assisted Computationally Simple PI$^\lambda$D$^\mu$ Control of a Quadrotor UAV , 2011, IEEE Transactions on Industrial Informatics.

[2]  Yangquan Chen,et al.  Necessary and sufficient stability condition of fractional-order interval linear systems , 2008, Autom..

[3]  Thierry Poinot,et al.  Fractional modelling and identification of thermal systems , 2011, Signal Process..

[4]  Xiao Mi,et al.  Fractional Order Sliding Mode Based Direct Power Control of Grid-Connected DFIG , 2018, IEEE Transactions on Power Systems.

[5]  Yoram Halevi,et al.  Fractional order control of flexible structures governed by the damped wave equation , 2015, 2015 American Control Conference (ACC).

[6]  B. Barmish.  A Generalization of Kharitonov's Four Polynomial Concept for Robust Stability Problems with Linearly Dependent Coefficient Perturbations , 1988 .

[7]  Shiqi Zheng,et al.  Robust stability of fractional order system with general interval uncertainties , 2017, Syst. Control. Lett..

[8]  Bilal Senol,et al.  Investigation of robust stability of fractional order multilinear affine systems: 2q2q-convex parpolygon approach , 2013, Syst. Control. Lett..

[9]  Mohammad Haeri,et al.  Robust stability testing function and Kharitonov-like theorem for fractional order interval systems , 2010 .

[10]  Jun-Guo Lu,et al.  Robust Stability and Stabilization of Fractional-Order Interval Systems with the Fractional Order $\alpha$: The $0≪\alpha≪1$ Case , 2010, IEEE Transactions on Automatic Control.

[11]  Jun-Guo Lu,et al.  Robust Stability and Stabilization of Fractional-Order Interval Systems: An LMI Approach , 2009, IEEE Transactions on Automatic Control.

[12]  Miguel Bernal,et al.  Comments on “Robust Stability and Stabilization of Fractional-Order Interval Systems With the Fractional Order $\alpha$: The $0<\alpha<1$ Case” , 2015, IEEE Transactions on Automatic Control.

[13]  Guanghui Sun,et al.  Engineering Notes Fractional-Order Tension Control Law for Deployment of Space Tether System , 2014 .

[14]  Zissimos P. Mourelatos,et al.  Application of Nonequidistant Fractional-Order Accumulation Model on Trajectory Prediction of Space Manipulator , 2016, IEEE/ASME Transactions on Mechatronics.

[15]  Bilal Senol,et al.  A numerical investigation for robust stability of fractional-order uncertain systems. , 2014, ISA transactions.

[16]  Nusret Tan,et al.  Robust stability analysis of fractional order interval polynomials. , 2009, ISA transactions.

[17]  Richard L. Magin,et al.  Fractional calculus models of complex dynamics in biological tissues , 2010, Comput. Math. Appl..

[18]  Zhe Gao,et al.  Robust stabilization criterion of fractional-order controllers for interval fractional-order plants , 2015, Autom..

[19]  Shiqi Zheng,et al.  Graphical tuning method of FOPID controllers for fractional order uncertain system achieving robust D ‐stability , 2016 .

[20]  Christophe Farges,et al.  A stability test for non-commensurate fractional order systems , 2010, Syst. Control. Lett..