Continuity of dynamical systems: A system theoretic approach

This paper studies continuity of linear time-invariant dynamical systems, defined in terms of the system’s behavior. This concept is related to parameter continuity of associated system representations. For the case at hand, these will be autoregressive (AR) representations. The main result states that a family of linear time-invariant systems, with uniformly bounded dimension of the state space, converges if and only if the systems admit a convergent full rank (AR) representation.