Lyapunov-Krasovskii Functionals of Robust Type and Their Legendre-Tau-Based Approximation

Lyapunov-Krasovskii functionals of robust type have recently been introduced for the stability analysis in time-delay systems. They are inspired by the wide-spread Lyapunov-Krasovskii functionals of complete type, but aim at improved robustness results. The present paper recaps the most important aspects and proposes a numerical method to solve the defning equation of these functionals numerically. The numerical method relies on a Legendre-tau-based ODE approximation of the time-delay system and has recently been shown to yield convincing results for the finite-dimensional approximation of Lyapunov-Krasovskii functionals of complete type. In the latter case, a Lyapunov equation has to be solved. In the case of Lyapunov-Krasovskii functionals of robust type, an algebraic Riccati equation has to be solved instead.