Quadratic controllability, strong controllability, and a related output feedback property

Quadratic controllability and strong controllability are the two system properties to be discussed for a special class of norm bounded uncertain linear systems. The main contribution of this paper is twofold. First we show that it is possible to reduce the problem of checking quadratic controllability or strong controllability of a given uncertain system to the same problem for a reduced order subsystem, which we call the essential subsystem. Then we use this result to examine a related output feedback property. Specifically, for a given uncertain system, we will answer the following question: What condition is necessary and sufficient for the existence of a dynamic output feedback controller such that the states of the closed-loop system converge to the origin with an arbitrarily fast rate? Our aim is to provide an insight and better understanding of uncertain systems through these results.