Controllability of linear time-varying systems with delay in control†

Abstract

This paper is concerned with the study of controllability of linear systems with delay in the control function. It has been illustrated that many of the techniques which proved to be useful in the study of linear systems with no delay (alman et al. 19G2, Kroindlcr and Sarachik 1964) can be generalized when dealing with systems having delay in the control. An explicit expression is given for transferring a given state to any desired state using minimum control energy. The corresponding conditions for linear time-invariant systems (ebakhy and Bayoumi 1971) are obtained as a special case. Extensions to multiple- delays systems are also included. A new degree of controllability is introduced and the corresponding criteria are obtained.