  This paper addresses the problems of stabilization, robust control, and
observer design for nonlinear systems. We build upon recently a proposed method
based on contraction theory and convex optimization, extending the class of
systems to which it is applicable. We prove converse results for mechanical
systems and feedback-linearizable systems. Next we consider robust control, and
give a simple construction of a controller guaranteeing an L2-gain condition,
and discuss connections to nonlinear H-infinity control. Finally, we discuss a
"duality" result between nonlinear stabilization problems and observer
construction, in the process constructing globally stable reduced-order
observers for a class of nonlinear systems.
