Global stabilization of feedforward systems with lower-order vector field

This paper considers the problem of global stabilization for a class of generalized feedforward systems whose nonlinearities are allowed to be lower-order growing, instead of higher-order or linear growing as required by most of the existing results. To solve the problem, a domination approach is developed based on the adding a power integrator technique and nested saturation method. The use of a homogeneous structure of controller enables us to relax the growth condition on the nonlinearities and hence enlarges the class of feedforward systems which are globally stabilizable by state feedback.

[1]  Mrdjan Jankovic,et al.  Integrator forwarding: A new recursive nonlinear robust design , 1997, Autom..

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

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

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

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

[6]  Mrdjan J. Jankovic,et al.  Constructive Nonlinear Control , 2011 .

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

[8]  Alberto Isidori,et al.  Nonlinear Control Systems II , 1999 .

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

[10]  Wei-Song Lin,et al.  Synthesis of upper-triangular non-linear systems with marginally unstable free dynamics using state-dependent saturation , 1999 .

[11]  A. Isidori,et al.  Robust global stabilization of a class of uncertain feedforward nonlinear systems , 2000 .

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

[13]  Heinz Unbehauen,et al.  Decentralized robust stabilization for large-scale feedforward non-linear systems , 2006 .

[14]  Frédéric Grognard,et al.  Global stabilization of feedforward systems with exponentially unstable Jacobian linearization , 1999 .

[15]  Alessandro Astolfi,et al.  Homogeneous Approximation, Recursive Observer Design, and Output Feedback , 2008, SIAM J. Control. Optim..

[16]  P. Kokotovic,et al.  Constructive Lyapunov stabilization of nonlinear cascade systems , 1996, IEEE Trans. Autom. Control..

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

[18]  A. Isidori.  Nonlinear Control Systems , 1985 .

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