Discounting the past in robust finite-state systems

In this paper we introduce discounted input-output dynamical stability as a variant of a recently introduced notion of robustness for discrete and cyber-physical systems. We analyze the verification and synthesis problems for this new notion of robustness for discrete systems given by finite-state automata. We show that the verification problem can be solved in terms of a linear program and hence is solvable in polynomial time. We provide an approximate solution to the synthesis problem whose complexity depends on the accuracy of the approximation. We discuss the merits and drawbacks of discounted input-output dynamical stability in comparison with existing robustness concepts for discrete systems.