UC Merced

This dissertation presents a series of studies on the analysis and control of time-delayed dynamical systems. We first review the discrete methods of semidiscretization and digital control approach. Then we introduce a new method of continuous time approximation (CTA) for the response of linear and nonlinear dynamical systems with time delay. We investigate the accuracy of temporal responses as well as the spectral properties of the CTA method, and present several variants of the CTA method with improved accuracy. Finally, we apply the CTA method to control problems of time-delayed systems including optimal control, supervisory control and sliding mode control of uncertain systems. The CTA method creates a set of state equations for the delayed portion of the response leading to a high and finite dimensional state space formulation of the time-delayed system. The resulting state equations are in the standard state space form, making all the existing solution methods and control design tools for linear and nonlinear dynamical systems amenable to time-delayed systems. The CTA method can handle multiple independent time delays in a natural way. The work in this dissertation indicates that the CTA method is a promising method for analysis and control design of complex nonlinear time-delayed dynamical systems.