Discretized Lyapunov functional for uncertain systems with multiple time-delay

The stability of uncertain systems with multiple time-delay is studied using a quadratic Lyapunov functional. By choosing piecewise linear parameters for the kernel of a quadratic Lyapunov functional, the guaranteed stability condition is formulated in the form of a linear matrix inequality. The extent of conservatism depends on the grid size. However, numerical results show that even a very coarse discretization can produce quite satisfactory results. The possibility of nonuniform grid size and more general Lyapunov functional is of interest even for single delay systems. Numerical examples are presented