Sampled data hereditary systems: feedback and optimization

The author reviews recent progress in the synthesis of controllers where the controlled system is a linear time-delay type. The controlled system can be modeled by linear differential difference equations, or equivalently by transfer functions which are ratios of exponential polynomials. Particular emphasis is placed on simplified methods of synthesis since even the quadratic theory of control of linear time-delay systems is quite involved. If one allows sampling in the control scheme, then the output from the system (sensed output) is monitored and reported only at discrete instants of time (sampling times) and the input to the continuous-time controlled system is maintained at a constant value between the sample times (by a zero-order hold circuit) and changed only at the sample times