Dissimilarity for Linear Dynamical Systems

We introduce backward dissimilarity (BD) for discrete-time linear dynamical systems (LDS), which relaxes existing notions of bisimulations by allowing for approximate comparisons. BD is an invariant property stating that the difference along the evolution of the dynamics governing two state variables is bounded by a constant, which we call dissimilarity. We demonstrate the applicability of BD in a simple case study and showcase its use concerning: (i) robust model comparison; (ii) approximate model reduction; and (iii) approximate data recovery. Our main technical contribution is a policy-iteration algorithm to compute BDs. Using a prototype implementation, we apply it to benchmarks from network science and discrete-time Markov chains and compare it against a related notion of bisimulation for linear control systems.