Disturbance Rejection for Fractional-Order Time-Delay Systems

This paper presents an equivalent-input-disturbance (EID-) based disturbance rejection method for fractional-order time-delay systems. First, a modified state observer is applied to reconstruct the state of the fractional-order time-delay plant. Then, a disturbance estimator is designed to actively compensate for the disturbances. Under such a construction of the system, by constructing a novel monochromatic Lyapunov function and using direct Lyapunov approach, the stability analysis and controller design algorithm are derived in terms of linear matrix inequality (LMI) technique. Finally, simulation results demonstrate the validity of the proposed method.

[1]  Guo-Ping Liu,et al.  Disturbance rejection for time-delay systems based on the equivalent-input-disturbance approach , 2014, J. Frankl. Inst..

[2]  R. Hilfer.  Applications Of Fractional Calculus In Physics , 2000 .

[3]  James Lam,et al.  State feedback H ∞ control of commensurate fractional-order systems , 2014, Int. J. Syst. Sci..

[4]  D. Ho,et al.  Robust stabilization for a class of discrete-time non-linear systems via output feedback: The unified LMI approach , 2003 .

[5]  P. Khargonekar,et al.  Robust stabilization of uncertain linear systems: quadratic stabilizability and H/sup infinity / control theory , 1990 .

[6]  Yangquan Chen,et al.  Computers and Mathematics with Applications Stability of Fractional-order Nonlinear Dynamic Systems: Lyapunov Direct Method and Generalized Mittag–leffler Stability , 2022 .

[7]  Yong Zhou,et al.  Non-fragile observer-based robust control for a class of fractional-order nonlinear systems , 2013, Syst. Control. Lett..

[8]  Yong-sheng Ding,et al.  A generalized Gronwall inequality and its application to a fractional differential equation , 2007 .

[9]  Yisheng Zhong,et al.  State feedback H∞ optimal control for linear fractional-order systems , 2010, Proceedings of the 29th Chinese Control Conference.

[10]  Dumitru Baleanu,et al.  LYAPUNOV-KRASOVSKII STABILITY THEOREM FOR FRACTIONAL SYSTEMS WITH DELAY , 2011 .

[11]  Omar Naifar,et al.  Comments on "Lyapunov stability theorem about fractional system without and with delay" , 2016, Commun. Nonlinear Sci. Numer. Simul..

[12]  Mingxing Fang,et al.  Improving Disturbance-Rejection Performance Based on an Equivalent-Input-Disturbance Approach , 2008, IEEE Transactions on Industrial Electronics.

[13]  Guoping Lu,et al.  Lyapunov stability theorem about fractional system without and with delay , 2015, Commun. Nonlinear Sci. Numer. Simul..

[14]  Alain Oustaloup,et al.  A Lyapunov approach to the stability of fractional differential equations , 2009, Signal Process..

[15]  M. Lazarevic.  Non-Lyapunov stability and stabilization of fractional order systems including time-varying delays , 2011 .

[16]  Ali Khaki Sedigh,et al.  Stabilization of multi-input hybrid fractional-order systems with state delay. , 2011, ISA transactions.

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

[18]  Mathieu Moze,et al.  On bounded real lemma for fractional systems , 2008 .

[19]  Alain Oustaloup,et al.  Frequency-band complex noninteger differentiator: characterization and synthesis , 2000 .

[20]  Jean-Pierre Richard,et al.  Time-delay systems: an overview of some recent advances and open problems , 2003, Autom..

[21]  Yong-Hong Lan,et al.  Observer-based robust control of a (1⩽ a ≪ 2) fractional-order uncertain systems: a linear matrix inequality approach , 2012 .

[22]  Min Wu,et al.  Active Disturbance Rejection Control Based on an Improved Equivalent-Input-Disturbance Approach , 2013, IEEE/ASME Transactions on Mechatronics.