Results on finite-time boundedness and finite-time control of non-linear quadratic systems subject to norm-bounded disturbances

The present study investigates the synthesis of sufficient conditions for finite-time boundedness and stabilisation of non-linear quadratic systems with exogenous disturbances. For this purpose, the usefulness of combining the notion of annihilator with a version of Finsler's lemma has been investigated. The obtained design conditions are expressed in terms of a set of state-dependent linear matrix inequalities. Several numerical examples are given to show the effectiveness of the authors' approach.

[1]  Yanjun Shen,et al.  Finite-time H∞ control for linear continuous system with norm-bounded disturbance , 2009 .

[2]  Francesco Amato,et al.  Sufficient Conditions for Finite-Time Stability and Stabilization of Nonlinear Quadratic Systems , 2010, IEEE Transactions on Automatic Control.

[3]  A. Trofino,et al.  LMI stability conditions for uncertain rational nonlinear systems , 2014 .

[4]  S. Bhat,et al.  Continuous finite-time stabilization of the translational and rotational double integrators , 1998, IEEE Trans. Autom. Control..

[5]  Gennaro Figalli,et al.  An optimal feedback control for a bilinear model of induction motor drives , 1984 .

[6]  F. Amato,et al.  Finite-time stability of linear systems: an approach based on polyhedral lyapunov functions , 2010 .

[7]  Shengyuan Xu,et al.  Finite-time boundedness and stabilisation for a class of non-linear quadratic time-delay systems with disturbances , 2013 .

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

[9]  Francesco Amato,et al.  Finite-Time Stability of Linear Time-Varying Systems: Analysis and Controller Design , 2010, IEEE Transactions on Automatic Control.

[10]  Ioan Doré Landau,et al.  Reduced order bilinear models for distillation columns , 1978, Autom..

[11]  Wilfrid Perruquetti,et al.  Finite time stability conditions for non-autonomous continuous systems , 2008, Int. J. Control.

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

[13]  Francesco Amato,et al.  Finite-time control for uncertain linear systems with disturbance inputs , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[14]  L. Weiss,et al.  ON THE STABILITY OF SYSTEMS DEFINED OVER A FINITE TIME INTERVAL. , 1965, Proceedings of the National Academy of Sciences of the United States of America.

[15]  F. Solimano,et al.  Global stability and oscillations in classical Lotka-Volterra loops , 1987 .