Control Strategy for Time-Delay Systems

Chapter Nine: Lambert W function approach to analysis and stabilization of time-delay systems

Niraj Choudhary; S. Janardhanan; Indra Narayan Kar    Department of Electrical Engineering, Indian Institute of Technology Delhi, New Delhi, India

Abstract

In this chapter, we address the Lambert W function approach for the analysis and design of multidimensional time-delay systems (TDSs). By considering a specific yet standard class of TDSs with $rank(A_d)=1$ we show that all the characteristic roots of the system can be associated with only the real branches of the Lambert W function as there does not exist a one-to-one correspondence between the characteristic ...