Estimating stable delay interval using discretized Lyapunov-Krasovskii functional method

The discretized Lyapunov-Krasovskii functional (DLF) method is asymptotically accurate in stability analysis for time-delay systems. In general, a system may have multiple stable delay intervals, and DLF is especially effective to study such systems. In this article, a DLF-based method is proposed to accurately estimate the maximum stable delay interval without using bisection, when one point in this interval is given. The formulation uses generalized eigenvalue problem (GEVP) of linear matrix inequalities (LMIs), and iterations may be used to reach the analytical limits either in finite number of steps or asymptotically. The coupled differential-difference equations are used to illustrate the method. However, the idea can be easily adapted to traditional differential-difference equation setting.