Controllability Analysis of Linear Time-Invariant Descriptor Systems∗

A canonical form for general linear time-invariant descriptor systems has been developed. Using this, it has been proved that complete controllability is equivalent to the reachable controllability plus controllability at infinity for general descriptor systems. Further, it has been proved that complete controllability is invariant under derivative as well as proportional state feedback while strong controllability is preserved under proportional state feedback but is not necessarily retained under derivative feedback. It is noteworthy that the aforesaid results are available for regular descriptor systems. We have extended these results for general descriptor systems. Examples are provided to illustrate the presented theory.