Discretization of Lyapunov functional for uncertain time-delay systems

The stability problem of uncertain time-delay systems is considered using a quadratic Lyapunov functional. The kernel of the Lyapunov functional is a vector valued function of two variables in a square domain. The domain is divided into a mesh of uniform triangles, and the kernel is chosen to be a continuous and piecewise second order polynomial. As a result, the stability criterion can be written in the form of a linear matrix inequality. The maximum time-delay for stability can also be directly calculated, and various extensions are possible