Discretized LMI set in the stability problem of linear uncertain time-delay systems

The stability problem of linear uncertain time-delay systems is considered using a quadratic Lyapunov functional. The resulting stability criterion is a constrained linear matrix inequality set. The condition is necessary and sufficient if it is applied to uncertainty-free systems. A discretization scheme is proposed to reduce the constrained LMI set to a regular LMI problem. Conservatism due to discretization can be made small through finer discretization. Comparison with a previous example shows significant improvements even under very coarse discretization.