A Lambert W function approach for decay function estimation in linear time delay systems

The estimation of the decay function (i.e. Ke^αt Φ) for time delay systems has been a long-standing problem. Most existing methods focus on dominant decay rate estimation based on either matrix measure/norm or Lyapunov function approaches and lead to conservative estimation. A new Lambert W function based approach for estimation of the decay function for time delay systems is presented. Using the proposed approach, the optimal decay rate and an estimate of the corresponding factor K can be obtained. Less conservative estimates of the decay function can lead to more accurate description of the exponential behavior of time delay systems, and more effective control design based on those results. The method is illustrated with a numerical example, and results compare favorably to other methods for decay function estimation.