摘要：AbstractConverse passivity theorems are established for finite-dimensional (FD) linear time-invariant (LTI) systems. Consider an FD LTI systemG1interconnected in positive feedback with another FD LTI systemG2. It is demonstrated that when the closed-loop system is (robustly) stable (in the sense of finiteL2gain) for arbitrary strictly passiveG2, then-G1must necessarily be passive. It is also demonstrated that when the closed-loop system is uniformly stable across the set of arbitrary passiveG2, then-G1must necessarily be strictly passive. The proofs are constructive; i.e., we show how to find a de-stabilizing FD LTIG2whenG1violates the necessity condition of stability.
