Delay-dependent stability analysis of linear systems with time-varying delay

Stability of time delay systems is investigated considering the delay-dependent case. The system without delays is assumed stable and conservative conditions are derived for finding the maximal delay that preserves stability. The problem is treated in the quadratic separation framework and the resulting criteria are formulated as feasibility problems of Linear Matrix Inequalities. The construction of the results relies on a fractioning of the delay. As the fractioning becomes thinner, the results prove to be less and less conservative. An example show the effectiveness of the proposed technique.