Effectivity of the stabilization of higher periodic orbits of chaotic maps

In many cases linear controllers are designed to stabilize nonlinear chaotic systems on periodic orbits. Paskota defined the neighbourhood size, i.e. a measure of the region where a linear controller can effectively stabilize a chaotic system on a fixed point. Generalizing this idea to the stabilization of higher periodic orbits, two performance measures-the neighbourhood size and the contracting region-are defined to determine the effectivity of a linear controller. This leads to a nonlinear constrained optimization problem, which, in general, has to be solved numerically. The effectivity of several linear controllers, when applied to the Henon map and the Ikeda map, is compared