Controllability, observability, pole allocation, and state reconstruction

In this paper we discuss the concepts of controllability, reachability, reconstructibility, and observability and attempt to show why these concepts are important in linear systems theory. We show how the above concepts allow us to solve the existence problem of closed-loop regulation of a linear time-invariant finite-dimensional system. The main results related to this are Theorems 4 and 5. Similar but less sharp results are also presented for time-varying systems. The discussion then proceeds to the precise relationships that exist between input-output and state descriptions of systems. Finally, the question of equivalence of internal and input-output stability is discussed.