Regularizability, controllability and observability of rectangular descriptor systems by dynamic compensation

Rectangular descriptor systems (RADS's) by dynamic compensation are studied in this paper. Some new notions about regularizability, impulse (I-) controllability and impulse (I-) observability, R-controllability and R-observability are introduced for RADS's in the sense of dynamic compensation. Similar definitions can further be given for admissibility and consistency of initial conditions. Equivalent conditions corresponding to these notions are derived. It is pointed out that the new notions are not contradictive to the existing ones. A necessary and sufficient condition is presented for the existence of a dynamic compensator such that the closed-loop system is regular, stable and impulse-free. It is shown that the duality on the conditions for freeness of impulse, I-(or R-) controllability and I-(or R-) observability for RADS's is true, and the symmetry of the properties for the systems between row and column also holds. This demonstrates that properties of RADS's are consistent with those of regular descriptor systems (RDS's) in form. Thus these new notions and results for RADS's are natural extension for those of RDS's.