Analysis and Control of Time Delay Systems Using the LambertWDDE Toolbox

Abstract

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.KeywordsTime Delay SystemDelay Differential EquationStability RadiusLinear Time Invariant SystemLinear Time InvariantThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.