Global Stabilization of a Class of High-Order Upper-Triangular Nonlinear Systems using Dynamic State-Feedback

Abstract: In this paper, we propose a control technique for a class of upper-triangular nonlinear systems, whose linearization about the origin is not guaranteed to be controllable, and the growth rate of nonlinear terms depends on the input. Based on the adding a power integrator technique and homogeneous domination approach, the state-feedback controller is recursively constructed such that all the signals of the closed-loop system are bounded and the system states converge to the zero globally asymptotically.

[1]  A. Teel.  Global stabilization and restricted tracking for multiple integrators with bounded controls , 1992 .

[2]  Xue-Jun Xie,et al.  Adaptive control for high‐order time‐delay uncertain nonlinear system and application to chemical reactor system , 2015 .

[3]  Chunjiang Qian,et al.  A homogeneous domination approach for global output feedback stabilization of a class of nonlinear systems , 2005, Proceedings of the 2005, American Control Conference, 2005..

[4]  Chunjiang Qian,et al.  Output Feedback Stabilization of Nonlinear Feedforward Systems using Low Gain Homogeneous Domination , 2007, 2007 IEEE International Conference on Control and Automation.

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

[6]  Jie Huang,et al.  Disturbance Attenuation of Feedforward Systems With Dynamic Uncertainty , 2008, IEEE Transactions on Automatic Control.

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

[8]  Wei Lin,et al.  Homogeneity with incremental degrees and global stabilisation of a class of high-order upper-triangular systems , 2012, Int. J. Control.

[9]  Chunjiang Qian,et al.  A generalised homogeneous solution for global stabilisation of a class of non-smooth upper-triangular systems , 2014, Int. J. Control.

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

[11]  Chunjiang Qian,et al.  An expanded method to robustly stabilize uncertain nonlinear systems , 2008, Commun. Inf. Syst..

[12]  L. Praly,et al.  Adding integrations, saturated controls, and stabilization for feedforward systems , 1996, IEEE Trans. Autom. Control..

[13]  Wei Lin,et al.  Adding one power integrator: a tool for global stabilization of high-order lower-triangular systems , 2000 .

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

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

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