Analysis of Linear Time Invariant Systems with Time Delay

Time Delay Control has recently been suggested as an alternative scheme for control of systems with unknown dynamics and unpredictable disturbances. The proposed control algorithm does neither require an explicit plant model nor depend on the estimation of specific plant parameters. Rather, it uses information in the recent past to directly estimate the unknown dynamics at any given instant, through time delay. In earlier papers, analysis and implementation of Time Delay Controller for nonlinear systems were discussed. This paper analyzes the continuous Time Delay Controller for a class of linear time-invariant (LTI) systems. LTI systems under Time Delay Control are described by LTI differential difference equations. Results of stability analysis are obtained using the properties of linear time-delayed systems. These results provide useful guidelines in design of the Time Delay Controller. The convergence of closed loop system error to zero for certain classes of inputs and disturbances when the system is stable is also established. A discussion is presented comparing Time Delay Control with Repetitive Control. Illustrative examples are included.