Passivity of Control Systems on Compact Manifolds

Surgery on Compact Manifolds

Invariant measures and controllability of finite systems on compact manifolds

A control system is said to be nite if the Lie algebra generated by its vector elds is nite dimensional. Su cient conditions for such a system on a compact manifold to be controllable are stated in terms of its Lie algebra. The proofs make use of the Equivalence Theorem of [7] and of the existence of an invariant measure on certain compact homogeneous spaces.

Passivity-Based Control of Switched Nonlinear Systems

Zusammenfassung Es wird eine konstruktive Reglerentwurfsmethode für schaltende nichtlineare steuerungssaffine Systeme vorgestellt, die dem geschlossenen Regelkreis eine schaltende Port-Hamiltonsche Struktur mit gemeinsamer Energiefunktion zuweist und so (asymptotische) Stabilität der Ruhelage erzielt. Die Methode generiert alle schaltenden Zustandsrückführungen, welche die Strecke unter beliebi...

The logarithmic HLS inequality for systems on compact manifolds

Lipschitz Spaces on Compact Manifolds

Let f be a bounded function on the real line IF!. One may characterize the structural properties off by the modulus of smoothness w(t,f) = sup{lf (4 -f( y)l; x, y E 08, I x y I < t>, and, if w(t) is a continuous nondecreasing function of t > 0 such that w(O) = 0, by the Lipschitz class Lip(w) which is the set of all continuous functions such that su~~<~<i w(t, f)/o(t) < 00. It is possible to ex...