ROBUST STABILITY CHECKING OF A CLASS OF LINEAR INTERVAL FRACTIONAL ORDER SYSTEM USING LYAPUNOV INEQUALITY

Abstract This paper provides a new analytical robust stability checking method of fractional-order linear time invariant interval uncertain system. This paper continues the authors’ previous work (Chen et al., 2005a) where matrix perturbation theory was used. For the new robust stability checking, Lyapunov inequality is utilized for finding the maximum eigenvalue of a Hermitian matrix. Through numerical examples, the usefulness and the effectiveness of the newly proposed method are verified.

[1]  Alain Oustaloup,et al.  On the CRONE Suspension , 2014 .

[2]  S. Manabe.  The non-integer integral and its application to control systems. , 1961 .

[3]  Xavier Moreau,et al.  The CRONE Suspension , 1996 .

[4]  Y. Chen,et al.  A comparative introduction of four fractional order controllers , 2002, Proceedings of the 4th World Congress on Intelligent Control and Automation (Cat. No.02EX527).

[5]  Mathukumalli Vidyasagar.  A characterization of e At and a constructive proof of the controllability criterion , 1971 .

[6]  José António Tenreiro Machado,et al.  Fractional signal processing and applications , 2003, Signal Process..

[7]  Yangquan Chen,et al.  Robust controllability of interval fractional order linear time invariant systems , 2006, Signal Process..

[8]  YangQuan Chen,et al.  Stability of linear time invariant systems with interval fractional orders and interval coefficients , 2004, Second IEEE International Conference on Computational Cybernetics, 2004. ICCC 2004..

[9]  Alain Oustaloup,et al.  The CRONE Control of Resonant Plants: Application to a Flexible Transmission , 1995, Eur. J. Control.

[10]  B. Molinari.  The stabilizing solution of the discrete algebraic riccati equation , 1975 .

[11]  Igor Podlubny,et al.  Fractional-order systems and PI/sup /spl lambda//D/sup /spl mu//-controllers , 1999 .

[12]  Alain Oustaloup,et al.  Fractional order sinusoidal oscillators: Optimization and their use in highly linear FM modulation , 1981 .

[13]  D. Matignon,et al.  Some Results on Controllability and Observability of Finite-dimensional Fractional Differential Systems , 1996 .

[14]  M. E. Bise,et al.  Fractional calculus application in control systems , 1990, IEEE Conference on Aerospace and Electronics.

[15]  J. Sabatier,et al.  LMI Tools for Stability Analysis of Fractional Systems , 2005 .

[16]  G. Hargreaves.  Interval Analysis in Matlab , 2002 .

[17]  M. Caputo.  Linear Models of Dissipation whose Q is almost Frequency Independent-II , 1967 .

[18]  A. Michel,et al.  Stability of viscoelastic control systems , 1987, 26th IEEE Conference on Decision and Control.

[19]  D. Matignon.  Stability properties for generalized fractional differential systems , 1998 .

[20]  I. Podlubny.  Fractional-order systems and PIλDμ-controllers , 1999, IEEE Trans. Autom. Control..

[21]  Manuel Ortigueira,et al.  Special Issue on Fractional signal Processing and applications , 2003 .

[22]  D. Matignon.  Stability results for fractional differential equations with applications to control processing , 1996 .

[23]  Lokenath Debnath,et al.  A brief historical introduction to fractional calculus , 2004 .

[24]  Yangquan Chen,et al.  Fractional Calculus and Biomimetic Control , 2004, 2004 IEEE International Conference on Robotics and Biomimetics.

[25]  Anissa Zergaïnoh-Mokraoui,et al.  State-space representation for fractional order controllers , 2000, Autom..

[26]  J. Partington,et al.  Coprime factorizations and stability of fractional differential systems , 2000 .

[27]  Yangquan Chen,et al.  Robust stability check of fractional order linear time invariant systems with interval uncertainties , 2005, IEEE International Conference Mechatronics and Automation, 2005.

[28]  S. Gutman,et al.  A general theory for matrix root-clustering in subregions of the complex plane , 1981 .