Generalized homogeneity with monotone degree and smooth stabilization for a class of feedforward systems

In this paper, by integrating the generalized homogeneity with monotone degrees (HWMD) with the top-bottom/bottom-top design strategy, we develop a new design procedure which enables us to explicitly construct global stabilizers for a class of feedforward systems. The proposed new control design strategy has several new features. First, a series of positive constant gains instead of positive function gains are updated to overcome the disadvantage caused by the variety of homogenous degrees. Second, the flexibility of HWMD provides a general framework to unify several existing results. Moreover, now it is possible to design continuously differentiable stabilizers for some feedforward systems for which only continuous stabilizers were previously designed.

[1]  P. Kokotovic,et al.  Global asymptotic stabilization of the ball-and-beam system , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

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

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

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

[5]  A. Teel.  Using Saturation to Stabilize a Class of Single-Input Partially Linear Composite Systems , 1992 .

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

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

[8]  R. Sepulchre,et al.  Lyapunov functions for stable cascades and applications to global stabilization , 1999, IEEE Trans. Autom. Control..

[9]  A. Teel.  A nonlinear small gain theorem for the analysis of control systems with saturation , 1996, IEEE Trans. Autom. Control..

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

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

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