ROBUST LFR-BASED TECHNIQUE FOR STABILITY ANALYSIS OF LIMIT CYCLES

Linear matrix inequality based techniques, most often used for robust analysis of linear systems, are applied to the stability analysis of periodic equilibrium trajectories of nonlinear systems. Results are derived by linearfractional representation of the nonlinearities and taking into account parametric uncertainties in the same time. Numerically exploitable formulas are obtained by discretization. An academic example illustrates the entire methodology.

[1]  D. Jordan,et al.  Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers , 1979 .

[2]  Gérard Scorletti,et al.  Control of rational systems using linear-fractional representations and linear matrix inequalities , 1996, Autom..

[3]  S. Hara,et al.  Well-posedness of feedback systems: insights into exact robustness analysis and approximate computations , 1998, IEEE Trans. Autom. Control..

[4]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[5]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

[6]  Nicole Imbert,et al.  Robustness Analysis of a Launcher Attitude Controller Via µ-Analysis , 2001 .

[7]  Pablo A. Iglesias,et al.  Robustness analysis of a self-oscillating molecular network in Dictyostelium discoideum , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[8]  Minyue Fu,et al.  Guaranteed cost control of uncertain nonlinear systems via polynomial lyapunov functions , 2002, IEEE Trans. Autom. Control..

[9]  Johan Löfberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004 .

[10]  C. W. Scherer,et al.  Relaxations for Robust Linear Matrix Inequality Problems with Verifications for Exactness , 2005, SIAM J. Matrix Anal. Appl..

[11]  D. Henrion,et al.  QUADRATIC SEPARATION FOR FEEDBACK CONNECTION OF AN UNCERTAIN MATRIX AND AN IMPLICIT LINEAR TRANSFORMATION , 2005 .

[12]  Jongrae Kim,et al.  Robustness analysis of linear periodic time-varying systems subject to structured uncertainty , 2006, Syst. Control. Lett..

[13]  Christophe Farges.  Méthodes d'analyse et de synthèse robustes pour les systèmes linéaires périodiques , 2006 .

[14]  Dimitri Peaucelle,et al.  Resilient structured periodic H2 synthesis for a spacecraft in elliptical orbits , 2007 .

[15]  D. Peaucelle,et al.  Periodic H2 synthesis for spacecraft in elliptical orbits with atmospheric drag and J2 perturbations , 2007, 2007 American Control Conference.

[16]  S. Bittanti,et al.  Periodic Systems: Filtering and Control , 2008 .