The Lambert W Function Approach to Time Delay Systems and the LambertW_DDE Toolbox

An overview of the recently developed Lambert W function approach for analysis and control of linear time invariant time delay systems (TDS) with a single known delay is provided. A solution via the Lambert W function is first presented for systems of order one, then extended to higher order systems using the matrix Lambert W function. Free and forced solutions, stability, observability, controllability, and observer and controller design via eigenvalue assignment can all be studied based on this framework. The use of the Matlab-based open source software in the LambertW_DDE Toolbox is introduced using examples.