DELAY-DEPENDENT ROBUST STABILITY OF TIME DELAY SYSTEMS

In this note, we provided an improved way of constructing a Lyapunov- Krasovskii functional for a linear time delay system. This technique is based on the reformulation of the original system and a discretization scheme of the delay. A hierarchy of Linear Matrix Inequality based results with increasing number of variables is given and is proved to have convergence properties in terms of conservatism reduction. Examples are provided which show the effectiveness of the proposed conditions.