Estimation of the domain of attraction for nonlinear autonomous systems using a bezoutian approach

One of the central subjects in modern control engineering is the investigation of stability for arbitrary given nonlinear systems. In this contribution we will introduce a novel method to compute the domain of attraction (DA) of a polynomial system using bezoutians. The presented method is able to estimate the DA for a given system linear as well as nonlinear system. It works for quadratic Lyapunov function as well as for arbitrary non linear Lyapunov functions. In this present algorithm the DA is successfully determined by an inner and outer bound. The inner bound yields an enclosure of the Lyapunov function (LF) countour line c*.

[1]  A. M. Lyapunov.  The general problem of the stability of motion , 1992 .

[2]  Bernd Tibken,et al.  An interval arithmetic approach for the estimation of the robust domain of attraction for nonlinear autonomous systems with nonlinear uncertainties , 2015, 2015 American Control Conference (ACC).

[3]  Kamil Fatih Dilaver.  Analyse der asymptotischen Stabilität nichtlinearer Systeme mit Hilfe des Satzes von Ehlich und Zeller , 2009 .

[4]  J. Sylvester,et al.  XVIII. On a theory of the syzygetic relations of two rational integral functions, comprising an application to the theory of Sturm’s functions, and that of the greatest algebraical common measure , 1853, Philosophical Transactions of the Royal Society of London.

[5]  A. Trofino.  Robust stability and domain of attraction of uncertain nonlinear systems , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[6]  Bernd Tibken,et al.  A new method to estimate a guaranteed subset of the domain of attraction for non-polynomial systems , 2012, 2012 American Control Conference (ACC).

[7]  Bernd Tibken,et al.  An interval arithmetic approach for the estimation of the domain of attraction , 2010, 2010 IEEE International Symposium on Computer-Aided Control System Design.

[8]  B. Tibken,et al.  Computing the domain of attraction for polynomial systems via BMI optimization method , 2006, 2006 American Control Conference.

[9]  B. Tibken,et al.  Estimation of the domain of attraction for polynomial systems using multidimensional grids , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[10]  G. Chesi.  Domain of Attraction: Analysis and Control via SOS Programming , 2011 .