Characterizations of Global Transversal Exponential Stability

We study the relationship between global exponential stability of an invariant manifold and existence a positive semidefinite Riemannian metric which is contracted by flow. In particular, we investigate how following properties are related to each other (in case): 1) A globally “transversally” exponentially stable; 2) corresponding variational system admits same property; 3) there exists degenerate flow can be used construct Lyapunov function. show that transverse contraction rate being larger than expansion shadow on sufficient condition for such An illustration these tools given in context full-order observer design.