In this paper, we present a Lyapunov function for systems containing a double integrator and with controller saturation. This Lyapunov function is composed of a positive-semide"nite quadratic term and an integral term. The main result provides a su$cient condition that guarantees a system with a double integrator can be globally stabilized by a saturating linear controller. For a triple-integra...

We develop an asynchronous time integration and coupling method with domain decomposition for linear and non-linear problems in mechanics. To ensure stability in the time integration and in coupling between domains, we use variational integrators with local Lagrange multipliers to enforce continuity at the domain interfaces. The asynchronous integrator lets each domain step with its own time st...

The understanding of mechanisms of higher brain functions expects a continuous reduction from higher activities to lower ones, eventually, to activities in individual neurons, expressed in terms of membrane potentials and ionic currents. While this approach is correct scientifically and desirable for applications, the complete range of the reduction is unavailable to a single researcher due to ...