Global finite-time stabilization of a class of upper-triangular systems

In this paper, we consider the problem of global finite-time stabilization for a class of upper-triangular systems. First, we use the generalized adding a power integrator technique to design a homogeneous controller which locally finite-time stabilizes the upper-triangular systems. Then, we integrate a series of nested saturation functions with the homogeneous controller and adjust the saturation level to ensure global attractivity. The combination of two steps yields the global finite-time stability of the considered upper-triangular systems.

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

[2]  Shihua Li,et al.  Global stabilization of feedforward systems with lower-order vector field , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[3]  Chunjiang Qian,et al.  A universal method for robust stabilization of nonlinear systems: unification and extension of smooth and non-smooth approaches , 2006, 2006 American Control Conference.

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

[5]  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..

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

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

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

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

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

[11]  Dennis S. Bernstein,et al.  Finite-Time Stability of Continuous Autonomous Systems , 2000, SIAM J. Control. Optim..

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

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

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

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

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