Developing and Automating Time Delay System Stability Analysis of Machinery Systems Using the Matrix Lambert W Function Method

Stability analysis of time delayed (TD) systems is not easy to conduct since the addition of delays within a dynamic model results in irrational system equations. Traditional analysis methods involve adding model approximates representing delays. These approximates make the system equations rational, but can drive stable TD systems to instability as approximate accuracy is improved. A more advanced method would be an invaluable tool for simplifying the stability analysis procedure for TD systems. A new method for analyzing TD system stability without adding TD approximates to the system has been presented by Asl et al. [1, 2]. This method involves using the Lambert W function to obtain analytic solutions for a set of delay differential equations. The research presented in this paper discusses the development and automation of TD system stability analysis for a complex machinery system utilizing this new method, the matrix Lambert W (MLW) function TD stability analysis method.