On convexity in stabilization of nonlinear systems

We recently derived a stability criterion for nonlinear systems, which can be viewed as a dual to Lyapunov's second theorem. The criterion has a physical interpretation in terms of the stationary density of a substance that is generated in all points of the state space and hows along the system trajectories. If the stationary density is finite everywhere except at a singularity in the origin, then almost all trajectories tend towards the origin. Here we consider consider state feedback for nonlinear systems and show that the search for a control law and density function that satisfy the convergence criterion can be stated in terms of convex optimization. The method is also applied to the problem of smooth blending of two given control laws.