Necessary and Sufficient Stability Criteria for a Class of Fractional-Order Delayed Systems

A new method for the stability analysis of a large class of fractional-order delayed systems is proposed. The exact region of the delay that can stabilize the system is determined without any approximation. Two steps of system transformation are employed to switch the fractional characteristic function to its corresponding integral function and to achieve an algebraic equation that facilitates the computation. Finally, an example is given to prove the feasibility of the proposed method.

[1]  I. Podlubny.  Fractional differential equations , 1998 .

[2]  Serdar Ethem Hamamci.  Stabilization using fractional-order PI and PID controllers , 2007 .

[3]  Soo-Chang Pei,et al.  Improved Methods for the Design of Variable Fractional-Delay IIR Digital Filters , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

[4]  Ivo Petrás,et al.  Fractional-Order Memristor-Based Chua's Circuit , 2010, IEEE Transactions on Circuits and Systems II: Express Briefs.

[5]  Z. H. Wang,et al.  A graphical test for the interval stability of fractional-delay systems , 2011, Comput. Math. Appl..

[6]  Liping Chen,et al.  Stability and Stabilization of a Class of Nonlinear Fractional-Order Systems With Caputo Derivative , 2012, IEEE Transactions on Circuits and Systems II: Express Briefs.

[7]  Rifat Sipahi,et al.  An exact method for the stability analysis of time-delayed linear time-invariant (LTI) systems , 2002, IEEE Trans. Autom. Control..

[8]  F. Mainardi,et al.  Recent history of fractional calculus , 2011 .

[9]  Hongjie Jia,et al.  A Simple Approach to Determine Power System Delay Margin , 2007, 2007 IEEE Power Engineering Society General Meeting.

[10]  Xiaozhong Liao,et al.  Robust stability criterion of fractional-order functions for interval fractional-order systems , 2013 .

[11]  Min Shi,et al.  An effective analytical criterion for stability testing of fractional-delay systems , 2011, Autom..

[12]  X.-L. Gao,et al.  H∞ desig with fractional-order P Dμ controllers , 2012 .

[13]  A. Uraz,et al.  An analysis stability test for a certain class of distributed parameter systems with delays , 1985 .

[14]  Masoud Karimi-Ghartemani,et al.  An efficient numerical algorithm for stability testing of fractional-delay systems. , 2009, ISA transactions.

[15]  Nejat Olgaç,et al.  An improved procedure in detecting the stability robustness of systems with uncertain delay , 2006, IEEE Transactions on Automatic Control.

[16]  Jun-Guo Lu,et al.  Stability Analysis of a Class of Nonlinear Fractional-Order Systems , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[17]  Mohammad Saleh Tavazoei,et al.  A proof for non existence of periodic solutions in time invariant fractional order systems , 2009, Autom..

[18]  Mehmet Önder Efe,et al.  Fractional Order Systems in Industrial Automation—A Survey , 2011, IEEE Transactions on Industrial Informatics.

[19]  Ivo Petras,et al.  Fractional-Order Nonlinear Systems , 2011 .

[20]  Chyi Hwang,et al.  A numerical algorithm for stability testing of fractional delay systems , 2006, Autom..

[21]  Ismail Ilker Delice,et al.  Advanced Clustering With Frequency Sweeping Methodology for the Stability Analysis of Multiple Time-Delay Systems , 2011, IEEE Transactions on Automatic Control.

[22]  Mohammad Haeri,et al.  Necessary and Sufficient Conditions for BIBO-Stability of Some Fractional Delay Systems of Neutral Type , 2011, IEEE Transactions on Automatic Control.