Title :
Extensions of classical averaging techniques to delay differential equations
Author :
Lehman, Brad ; Kolmanovskii, Vladimir B.
Author_Institution :
Dept. of Electr. & Comput. Eng., Mississippi State Univ., MS, USA
Abstract :
This paper extends the method of averaging due to Krylov and Bogoliubov (1947) and Bogoliubov and Mitropolskii (1961) to delay differential equations. Near identity change of variables are used to transform time varying delay differential equations into autonomous delay differential equations plus small perturbations. Then Lyapunov functionals are used to relate the autonomous averaged delay differential equation to the original time varying delay differential equation
Keywords :
Lyapunov methods; delays; differential equations; time-varying systems; Lyapunov functionals; autonomous averaged delay-differential equation; classical averaging techniques; small perturbations; time-varying delay-differential equation transformation; Adaptive control; Aging; Bifurcation; Delay effects; Differential equations; Mathematics; Stability analysis; Transforms; Vibration control;
Conference_Titel :
Decision and Control, 1994., Proceedings of the 33rd IEEE Conference on
Conference_Location :
Lake Buena Vista, FL
Print_ISBN :
0-7803-1968-0
DOI :
10.1109/CDC.1994.410893
