Interval Homogeneity-Based Control for a Class of Nonlinear Systems With Unknown Power Drifts

This technical note considers the global stabilization problem for a class of nonlinear systems with unknown power (exponent) drifts. Based on the concept of interval homogeneity with monotone degrees, the allowable bounds of the unknown power drifts can be explicitly determined to guarantee the solvability of the problem. The technique of adding a power integrator is revamped based on a new Lyapunov function with interval parameters and is recursively employed to construct a global stabilizer for the nonlinear systems.

[1]  Sergey Dashkovskiy,et al.  Robust Stabilization of the Generalized Triangular Form Nonlinear Systems With Disturbances , 2014, IEEE Transactions on Automatic Control.

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

[3]  M. Kawski.  Stabilization of nonlinear systems in the plane , 1989 .

[4]  Wei Lin,et al.  Homogeneous observers, iterative design, and global stabilization of high-order nonlinear systems by smooth output feedback , 2004, IEEE Trans. Autom. Control..

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

[6]  Zhao Wang,et al.  Reduced-order observer and controller design for a 1000MW ultra-supercritical unit , 2015 .

[7]  I. Kolmanovsky,et al.  Nonsmooth stabilization of an underactuated unstable two degrees of freedom mechanical system , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[8]  J. Tsinias,et al.  Explicit formulas of feedback stabilizers for a class of triangular systems with uncontrollable linearization , 1999 .

[9]  J. Coron,et al.  Lyapunov design of stabilizing controllers for cascaded systems , 1991 .

[10]  Wei Lin,et al.  On p-normal forms of nonlinear systems , 2003, IEEE Trans. Autom. Control..

[11]  L. Rosier.  Homogeneous Lyapunov function for homogeneous continuous vector field , 1992 .

[12]  A. Bacciotti,et al.  Liapunov functions and stability in control theory , 2001 .

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

[14]  Chunjiang Qian,et al.  Global stabilization of inherently non-linear systems using continuously differentiable controllers , 2014 .

[15]  Wolfgang Hahn,et al.  Stability of Motion , 1967 .

[16]  Wei Lin,et al.  Robust output feedback stabilization of uncertain nonlinear systems with uncontrollable and unobservable linearization , 2005, IEEE Transactions on Automatic Control.