Stabilizability of nonlinear infinite dimensional switched systems by measures of noncompactness in the space

This article studies the problem of stabilizability of nonlinear infinite dimensional switched systems. The switching rule is arbitrary and takes place between a countably infinite number of subsystems, each of which is represented by a differential equation in some Banach space. Using a topological notion of a (locally finite) cover and the Hausdorff measure of noncompactness in the c 0 space, we show how the problem of approximate stabilizability of switched systems can be cast into a sequential framework and dealt with. Examples of application are given.