BASIS MATRIX CHARACTERIZATION OF CONTROLLABILITY SUBSPACES

The Kronecker canonical form of the input-state pencil sN-NA is used in the derivation of the basis matrix description of the polynomial vectors p(s) lying in the kernel space of sN-NA; starting from that description of the vectors p(s), the basis matrix characterization of controllability subspaces (c.s.) (Verdulekie 1978) follows in a simple yet general way. The significance of the matrix characterization of C.8. extends beyond the computational aspects of C.B.; using arguments based on the special structure of the basis matrix, simple proofs of the Warren and Eckberg (1975) results are given. © 1974 Taylor & Francis Group, LLC.