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 expression, the guaranteed stability condition is formulated in the form of 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 non-uniform grid size and more general Lyapunov functional is of interest even for a single delay system. Numerical examples are presented.