Necessary and sufficient conditions for quadratic controllability of a class of uncertain systems

We introduce a controllability notion for uncertain systems, namely, quadratic controllability. For a specific class of norm bounded uncertain systems, we show that this notion is equivalent to controllability of a nominal system and the satisfaction of a certain structural condition by the uncertainty. For systems in which the uncertain parameters affect all control inputs, this structural condition is simply the familiar matching condition commonly encountered in the literature on robust and adaptive control of uncertain systems.