On complete Lyapunov-Krasovskii functional techniques for uncertain systems with fast-varying delays

Emilia Fridman (1) , Silviu-Iulian Niculescu (2)

1 Department of Electrical Engineering
2 L2S - Laboratoire des signaux et systèmes

Stability of linear systems with norm-bounded uncertainties and uncertain time-varying delays is considered. The delay is supposed to be bounded and fast varying (without any constraints on the delay derivative). Sufficient stability conditions are derived by direct Lyapunov method based on the complete Lyapunov-Krasovskii functional (LKF). A novel complete LKF construction is presented the derivative condition for the nominal LKF (i.e. for the LKF, which corresponds to the system with the nominal values of the coefficients and of the delay) depends on the 'present' state only. The comprehensive technique for stability analysis of uncertain time-delay systems is extended to the case of complete LKF the application of free weighting matrices (instead of descriptor model transformation) and of Jensen's inequality (instead of the cross-terms bounding). Numerical examples illustrate the efficiency of the method, and complete the paper. Copyright (c) 2007 John Wiley and Sons, Ltd.

Mots clés: time-varying delay; norm-bounded uncertainties; Lyapunov-Krasovskii method

Domaines: Automatique

Emilia Fridman, Silviu-Iulian Niculescu. On complete Lyapunov-Krasovskii functional techniques for uncertain systems with fast-varying delays. International Journal of Robust and Nonlinear Control, 2008, 18 (3), pp.364-374. ⟨10.1002/rnc.1230⟩. ⟨hal-02195962⟩