Analysis and control of time delayed systems via the Lambert W function

This paper summarizes recent research results by the authors for the analytical solution to systems of delay differential equations using the matrix Lambert W function, and its applications to analysis and control of time-delay systems. The solution has the form of an infinite series of modes written in terms of the matrix Lambert W function. This solution is analytical in terms of the parameters, coefficients and delay time, of the system, and each eigenvalue in the infinite eigenspectrum is distinguished in terms of the branches of the Lambert W function. This enables extension of methods for systems of ordinary differential equations to systems of delay differential equations. These include stability analysis, controllability and observability, as well as methods for eigenvalue assignment. Copyright © 2007 International Federation of Automatic Control All Rights Reserved.