S. Nicaise, J. Valein, E. Fridman
tlooto Summary
Exponential stability analysis via Lyapunov method is extended to 1D heat and wave equations with time-varying delay in boundary conditions.
Abstract
Exponential stability analysis via Lyapunov method is extended to the one-dimensional heat and wave equations with time-varying delay in the boundary conditions. The delay function is admitted to be time-varying with an a priori given upper bound on its derivative, which is less than $1$. Sufficient and explicit conditions are derived that guarantee the exponential stability. Moreover the decay rate can be explicitly computed if the data are given.
Citation format
NICAISE, S.; VALEIN, J.; FRIDMAN, E. STABILITY OF THE HEAT AND OF THE WAVE EQUATIONS WITH BOUNDARY TIME-VARYING DELAYS. Discrete and Continuous Dynamical Systems-Series S, 2009, 2: 559–581.