Abstract
Converse passivity theorems are established for finite-dimensional (FD) linear time-invariant (LTI) systems. Consider an FD LTI system G1 interconnected in positive feedback with another FD LTI system G2. It is demonstrated that when the closed-loop system is (robustly) stable (in the sense of finite L2 gain) for arbitrary strictly passive G2, then -G1 must necessarily be passive. It is also demonstrated that when the closed-loop system is uniformly stable across the set of arbitrary passive G2, then -G1 must necessarily be strictly passive. The proofs are constructive; i.e., we show how to find a de-stabilizing FD LTI G2 when G1 violates the necessity condition of stability.
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