Abstract: Based on the Lyapunov functional， exponential stability for linear systems with timevarying delay was studied. The time delay is a differentiable function belonging to a given interval. A new criterion for exponential stability was proposed in the form of linear matrix inequalities. When the derivative of the Lyapunov functional was estimated， a tighter upper bound was obtained using convex combination and reciprocally convex combination approaches that led to less conservatism of the condition for exponential stability.In addition， the obtained exponential upper bound of the state depended only on the initial function itself. An example was then presented to show the effectiveness of the proposed method.

Key words: timevarying delay, exponential stability, linear matrix inequalities, reciprocally convex combination, Lyapunov functional