The uniform stabilizability and the margin of stabilizability for the approximations of infinite dimensional systems

The authors consider the use of stabilizability margins for finite-dimensional control systems, derived from an infinite-dimensional control system via an approximation scheme, as a tool to verify the uniform stabilizability of the finite-dimensional systems. It is shown that the relationship between the uniform stabilizability and the stabilizability margin of the matrix representation for approximate control systems depends on the norm used in different approximation subspaces relative to the norm induced by the original infinite-dimensional state space. The uniform norm equivalence condition is not satisfied in most of the commonly used approximation schemes. However, a simple change of variable can be helpful in establishing this condition in some cases