TY - JOUR
T1 - Stability of systems with uncertain delays
T2 - A new "complete" Lyapunov-Krasovskii functional
AU - Fridman, Emilia
N1 - Funding Information:
Manuscript received March 28, 2004; revised August 30, 2004 and November 16, 2005. Recommended by Associate Editor S.-I. Niculescu. This work was supported by the Kamea Fund of Israel. E. Fridman is with the Department of Electrical Engineering-Systems, Tel Aviv University, Tel-Aviv 69978, Israel (e-mail: emilia@eng.tau.ac.il). Digital Object Identifier 10.1109/TAC.2006.872769
PY - 2006/5
Y1 - 2006/5
N2 - Stability of linear systems with uncertain time-varying delay is considered in the case, where the nominal value of the delay is constant and nonzero. Recently a new construction of Lyapunov-Krasovskii functionals (LKFs) has been introduced: To a nominal LKF, which is appropriate to the system with nominal delays, terms are added that correspond to the perturbed system and that vanish when the delay perturbations approach 0. In the present note we combine a "complete" nominal LKF, the derivative of which along the trajectories depends on states and their derivatives, with the additional terms depending on the delay perturbation. The new method is applied to the case of multiple uncertain delays with one nonzero nominal value. Numerical examples illustrate the efficiency of the method.
AB - Stability of linear systems with uncertain time-varying delay is considered in the case, where the nominal value of the delay is constant and nonzero. Recently a new construction of Lyapunov-Krasovskii functionals (LKFs) has been introduced: To a nominal LKF, which is appropriate to the system with nominal delays, terms are added that correspond to the perturbed system and that vanish when the delay perturbations approach 0. In the present note we combine a "complete" nominal LKF, the derivative of which along the trajectories depends on states and their derivatives, with the additional terms depending on the delay perturbation. The new method is applied to the case of multiple uncertain delays with one nonzero nominal value. Numerical examples illustrate the efficiency of the method.
KW - Lyapunov-Krasovskii method
KW - Stability
KW - Time-varying delay
KW - Uncertain delay
UR - http://www.scopus.com/inward/record.url?scp=33646938706&partnerID=8YFLogxK
U2 - 10.1109/TAC.2006.872769
DO - 10.1109/TAC.2006.872769
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AN - SCOPUS:33646938706
VL - 51
SP - 885
EP - 890
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
SN - 0018-9286
IS - 5
ER -