Structural stability of linear dynamically varying (LDV) controllers

Linear dynamically varying (LDV) controllers have been shown to be useful in controlling nonlinear dynamical systems on compact sets, especially chaotic systems. In this paper it is shown that the ability to stabilize a dynamical system with an LDV controller is structurally stable in the C¹ topology, the Lipschitz topology and, in a restricted sense, the C⁰ topology provided that these systems are near enough to an LDV stabilizable C¹ dynamical system. Furthermore, the optimal LDV controller is shown to depend continuously on the dynamical system