Abstract
This paper considers the robust stability of the interconnection ofa linear time-invariant nominal system and uncertainty in the behavioral framework. We introduce the notion of half-line $\Phi$-nonnegativity that corresponds to the traditional passivity with respect to a quadratic supply rate. It is shown that, for the half-line $(-\Phi)$-nonnegative uncertainty, the uncertain interconnection is a regular interconnection and robustly stable if and only if the nominal system is half-line $\Phi$-positive. The present result is a generalization of the robust stability condition of a feedback system based the small gain or passivity theorem.
