Finite-Time Stabilization of Linear Time-Varying Continuous Systems

In this technical note, the problem of finite time stabilization of linear time-varying continuous systems is considered. Necessary and sufficient conditions, based upon the solution to some Lyapunov differential matrix equations, are proposed for particular cases of interest. From these conditions, the design of time-varying state feedback controller guaranteeing the finite time closed-loop stability is presented. Numerical experiments illustrate the potentialities of the approach.

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

[2]  Panos J. Antsaklis,et al.  Linear Systems , 1997 .

[3]  Guoshan Zhang,et al.  Finite-time stability and stabilization of linear stochastic systems , 2010, Proceedings of the 29th Chinese Control Conference.

[4]  Ping Lu,et al.  Closed-form control laws for linear time-varying systems , 2000, IEEE Trans. Autom. Control..

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

[6]  Sophie Tarbouriech,et al.  Control of Uncertain Systems with Bounded Inputs , 1997 .

[7]  R. Kálmán.  LYAPUNOV FUNCTIONS FOR THE PROBLEM OF LUR'E IN AUTOMATIC CONTROL. , 1963, Proceedings of the National Academy of Sciences of the United States of America.

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

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

[10]  Sophie Tarbouriech,et al.  Advanced strategies in control systems with input and output constraints , 2007 .

[11]  Henry D'Angelo,et al.  Linear time-varying systems : analysis and synthesis , 1970 .

[12]  G. Stewart,et al.  Matrix Perturbation Theory , 1990 .

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

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

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

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

[17]  V. Koltchinskii,et al.  Statistical learning methods in linear algebra and control problems: the example of finite-time control of uncertain linear systems , 2002 .

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

[19]  R. Stephenson.  A and V , 1962, The British journal of ophthalmology.

[20]  F. Amato,et al.  Finite-time control of linear time-varying systems via output feedback , 2005, Proceedings of the 2005, American Control Conference, 2005..