Quadratic CLFs for Koopman bilinear systems imply constant-input stabilizability, exactly characterized by a QCQP with a convex SDP relaxation as a sufficient test.
Necessary and sufficient conditions for rank-one-generated cones,
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On the Existence of Quadratic Control Lyapunov Functions for Koopman-Operator based Bilinear Systems
Quadratic CLFs for Koopman bilinear systems imply constant-input stabilizability, exactly characterized by a QCQP with a convex SDP relaxation as a sufficient test.