Summary: This chapter provides an overview of the Lambert W function approach. The approach has been developed for analysis and control of linear time-invariant time delay systems with a single known delay. A solution in the time-domain is given in terms of an infinite series, with the important characteristic that truncating the series provides a dominant solution in terms of the rightmost eigenvalues. A solution via the Lambert W function approach is first presented for systems of order one, then extended to higher order systems using the matrix Lambert W function. Free and forced solutions are used to investigate key properties of time-delay systems, such as stability, controllability and observability. Through eigenvalue assignment, feedback controllers and state-observers are designed. All of these can be achieved using the Lambert W function-based framework. The use of the MATLAB-based open source software in the LambertWDDE Toolbox is also introduced using numerical examples.
For the entire collection see [Zbl 1275.93004].