Boundary Stabilization of the Time Fractional Korteweg-de Vries-Burgers Equation

In this paper, we consider boundary stabilization for the time fractional Korteweg-de Vries-Burgers equation under a sector feedback control. Under the nonlinear controller satisfying a sector condition, the Mittag-Leffler stability of the closed-loop system is established by the fractional Lyapunov method.

[1]  J. F. Gómez‐Aguilar,et al.  On exact solutions for time-fractional Korteweg-de Vries and Korteweg-de Vries-Burger’s equations using homotopy analysis transform method , 2020 .

[2]  K. Saad,et al.  New fractional derivatives applied to the Korteweg–de Vries and Korteweg–de Vries–Burger’s equations , 2018 .

[3]  K. Saad,et al.  New fractional derivatives applied to the Korteweg–de Vries and Korteweg–de Vries–Burger’s equations , 2018, Computational and Applied Mathematics.

[4]  Lucie Baudouin,et al.  Two Approaches for the Stabilization of Nonlinear KdV Equation With Boundary Time-Delay Feedback , 2017, IEEE Transactions on Automatic Control.

[5]  C. Jia Boundary feedback stabilization of the Korteweg–de Vries–Burgers equation posed on a finite interval , 2016 .

[6]  J. H. Rodrigues,et al.  Global well-posedness and exponential decay rates for a KdV–Burgers equation with indefinite damping , 2014 .

[7]  Tielong Shen,et al.  Absolute stability of the Kirchhoff string with sector boundary control , 2014, Autom..

[8]  Jean-Michel Coron,et al.  Local rapid stabilization for a Korteweg–de Vries equation with a Neumann boundary control on the right , 2013, 1311.4031.

[9]  Bing-Yu Zhang,et al.  Boundary Stabilization of the Korteweg-de Vries Equation and the Korteweg-de Vries-Burgers Equation , 2012, Acta Applicandae Mathematicae.

[10]  A. Alikhanov A priori estimates for solutions of boundary value problems for fractional-order equations , 2010, 1105.4592.

[11]  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 .

[12]  J. Negro,et al.  Travelling wave solutions of two-dimensional Korteweg-de Vries-Burgers and Kadomtsev-Petviashvili equations , 2006 .

[13]  Ruth F. Curtain,et al.  Absolute-stability results in infinite dimensions , 2004, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[14]  Tingshu Hu,et al.  Absolute stability with a generalized sector condition , 2004, IEEE Transactions on Automatic Control.

[15]  PooGyeon Park,et al.  Stability criteria of sector- and slope-restricted Lur'e systems , 2002, IEEE Trans. Autom. Control..

[16]  Miroslav Krstic,et al.  Boundary control of the Korteweg-de Vries-Burgers equation: further results on stabilization and well-posedness, with numerical demonstration , 2000, IEEE Trans. Autom. Control..

[17]  Ragnar Winther,et al.  The Korteweg–de Vries Equation, Posed in a Quarter-Plane , 1983 .

[18]  Bao-Zhu Guo,et al.  Absolute boundary stabilization for an axially moving Kirchhoff beam , 2021, Autom..

[19]  P. Olver Nonlinear Systems , 2013 .

[20]  M. Aassila Stabilization of the Korteweg-de Vries-Burgers equation with non-periodic boundary feedbacks , 2003 .

[21]  Ruth F. Curtain,et al.  Absolute stability results for well-posed infinite-dimensional systems with applications to low-gain integral control , 2000 .

[22]  M. Krstić,et al.  Global Boundary Stabilization of the Korteweg-de Vries-Burgers Equation , 1998 .

[23]  H. Grad,et al.  Unified Shock Profile in a Plasma , 1967 .

[24]  A C Scott,et al.  Korteweg-de Vries Equation , 2022 .