On the Inverse of Linear Dynamical Systems

The problem considered is that of determining the inverse of a linear time-invariant dynamical system characterized by a first-order vector differential equation. This problem has application to various problems in control and estimation, where a state space representation is utilized. A necessary and sufficient condition is given for the existence of an inverse system and an algorithm is developed for the inverse system when one exists. The inverse algorithm generates a system composed of a differentiation system cascaded with a dynamical system.