SIAM Journal on Control and Optimization
The Dynamics of Control
A Converse Lyapunov Theorem for Linear Parameter-Varying and Linear Switching Systems
SIAM Journal on Control and Optimization
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This paper classifies continuous linear flows using concepts and techniques from topological dynamics. Specifically, the concepts of equivalence and conjugacy are adapted to flows on vector bundles, and the Lyapunov decomposition is characterized using the induced flows on the Grassmann and the flag bundles. These results are then applied to bilinear control systems, for which their behavior in $ \mathbb{R}^{d} $ , on the projective space $\mathbb{P}^{{d{\text{ - 1}}}} $ , and on the Grassmannians is characterized.