Kybernetika 37 no. 4, 479-504, 2001

Discretization schemes for Lyapunov-Krasovskii functionals in time-delay systems

Keqin Gu


This article gives an overview of discretized Lyapunov functional methods for time-delay systems. Quadratic Lyapunov-Krasovskii functionals are discretized by choosing the kernel to be piecewise linear. As a result, the stability conditions may be written in the form of linear matrix inequalities. Conservatism may be reduced by choosing a finer mesh. Simplification techniques, including elimination of variables and using integral inequalities are also discussed. Systems with multiple delays and distributed delays are also treated. Finally, the treatment of uncertainties and input-output performance requirements are discussed.