Finite-time stabilization of non affine systems a constructive method for polynomial systems

In this paper finite-time stabilization of nonlinear non affine systems, is considered. First we provide a formula for a finite time stabilizing state feedback control law, for a second order polynomial system. Then we extend the result to the case of polynomial systems with multiple inputs. Some extensions concerning asymptotic stabilization are given.

[1]  L. Weiss Converse Theorems for Finite Time Stability , 1968 .

[2]  P. Dorato,et al.  Finite time stability under perturbing forces and on product spaces , 1967, IEEE Transactions on Automatic Control.

[3]  Eduardo Sontag A universal construction of Artstein's theorem on nonlinear stabilization , 1989 .

[4]  Germain Garcia,et al.  Practical stability and stabilization of linear systems , 2009, 2009 17th Mediterranean Conference on Control and Automation.

[5]  Sophie Tarbouriech,et al.  Finite-Time Stabilization of Linear Time-Varying Continuous Systems , 2009, IEEE Transactions on Automatic Control.

[6]  Anthony N. Michel,et al.  On the bounds of the trajectories of differential systems , 1969 .

[7]  Wilfrid Perruquetti,et al.  On practical stability with the settling time via vector norms , 1995 .

[8]  L. Grujic On practical stability , 1973 .

[9]  F. G. Garashchenko Study of practical stability problems by numerical methods and optimization of beam dynamics , 1987 .

[10]  A. Michel,et al.  Practical Stability and Finite-Time Stability of Discontinuous Systems , 1972 .

[11]  Dennis S. Bernstein,et al.  Robust nonlinear control of the electromagnetically controlled oscillator , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[12]  Carlo Cosentino,et al.  Finite-time stabilization via dynamic output feedback, , 2006, Autom..

[13]  Francesco Amato,et al.  Necessary and sufficient conditions for finite-time stability of linear systems , 2003, Proceedings of the 2003 American Control Conference, 2003..

[14]  V. Lakshmikantham,et al.  Practical Stability Of Nonlinear Systems , 1990 .

[15]  P. Dorato SHORT-TIME STABILITY IN LINEAR TIME-VARYING SYSTEMS , 1961 .

[16]  Francesco Amato,et al.  Finite-time control of linear systems subject to parametric uncertainties and disturbances , 2001, Autom..