Analysis and control of time delay systems using the LambertWDDE Toolbox 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.

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