Minimum Time Settling of the Linear Sampled-Data System with Time Delay

Abstract

This paper is concerned with fundamental problems arising in the control of a linear sampled-data system with time-delay. An important and unsolved problem of such a system is the problem of finite time settling; namely, the problem of transferring the state of the system from an arbitrary initial state to an equilibrium state in a finite number of steps.
In this paper, the problem is solved by transforming the given system into a higher order sampled-data system without time-delay. The state transition matrix of the derived sampled-data system may be nonsingular or singular, depending on the structure of the original system.
In both cases, the problems of controllability and minimum time control are considered in detail. Finally, a numerical example is given.