Global stabilization via nested saturation function for high‐order feedforward nonlinear systems with unknown time‐varying delays

Summary We consider the global stabilization problem for a class of high-order feedforward time-delay nonlinear systems. The nested saturation function method is inherently improved to develop a continuous controller, without the requirements on the memory of the past input and the prior information of the time-varying delays. The proposed controller is less conservative in terms of the level of nonlinearities whose upper bounds include high-order, low-order, and linear terms. The design procedures are provided based on the sign function technique, the homogeneous domination idea, and the search of Lyapunov function. Finally, a simulation example is used to demonstrate the application of the obtained theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.

[1]  Shihua Li,et al.  Global smooth stabilization of a class of feedforward systems under the framework of generalized homogeneity with monotone degrees , 2013, J. Frankl. Inst..

[2]  Huawen Ye,et al.  Saturated Delayed Controls for Feedforward Nonlinear Systems , 2014, IEEE Transactions on Automatic Control.

[3]  C. Qian,et al.  Global output feedback stabilization of upper‐triangular nonlinear systems using a homogeneous domination approach , 2006 .

[4]  Kemei Zhang,et al.  A new approach to finite-time adaptive stabilization of high-order uncertain nonlinear system , 2015, Autom..

[5]  Qingrong Liu,et al.  Design of stabilizing controllers of upper triangular nonlinear time-delay systems , 2015, Syst. Control. Lett..

[6]  Xue-Jun Xie,et al.  Global continuous output-feedback stabilization for a class of high-order nonlinear systems with multiple time delays , 2014, J. Frankl. Inst..

[7]  Wei Lin,et al.  A continuous feedback approach to global strong stabilization of nonlinear systems , 2001, IEEE Trans. Autom. Control..

[8]  Yiguang Hong,et al.  Adaptive finite-time control of nonlinear systems with parametric uncertainty , 2006, IEEE Transactions on Automatic Control.

[9]  Luc Baron,et al.  Feedback stabilization for high order feedforward nonlinear time-delay systems , 2011, Autom..

[10]  M. P. Tzamtzi,et al.  An explicit formula of bounded feedback stabilizers for feedforward systems , 2001, Syst. Control. Lett..

[11]  Frédéric Mazenc,et al.  Tracking trajectories of the cart-pendulum system , 2003, Autom..

[12]  Chunjiang Qian,et al.  Global stabilization of a class of upper‐triangular systems with unbounded or uncontrollable linearizations , 2011 .

[13]  Yungang Liu,et al.  Global Finite-Time Stabilization via Time-Varying Feedback for Uncertain Nonlinear Systems , 2014, SIAM J. Control. Optim..

[14]  Ye Xudong,et al.  Brief Universal stabilization of feedforward nonlinear systems , 2003 .

[15]  Cong-Ran Zhao,et al.  Global stabilization of stochastic high-order feedforward nonlinear systems with time-varying delay , 2014, Autom..

[16]  Shihua Li,et al.  Global Stabilization of a Class of Feedforward Systems with Lower-Order Nonlinearities , 2010, IEEE Transactions on Automatic Control.

[17]  L. Baron,et al.  Asymptotic stabilization of high‐order feedforward systems with delays in the input , 2010 .

[18]  Zong-Yao Sun,et al.  New results on global stabilization for time‐delay nonlinear systems with low‐order and high‐order growth conditions , 2015 .

[19]  Luc Baron,et al.  Design of Stabilizing Controllers With a Dynamic Gain for Feedforward Nonlinear Time-Delay Systems , 2011, IEEE Transactions on Automatic Control.

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