Stability, controllability, and observability criteria for state-space dynamical systems on measure chains with an application to fixed point arithmetic

In this paper, our main attempt is to unify results on stability, controllability, and observability criteria on real-time dynamical systems with non-uniform domains. The results of continuous/discrete systems will now become a particular case of our results. As an application a first-order time scale dynamical system on measure chains in one-dimensional state space having both continuous/discrete filters to minimize the effect of a round of noise at the filter outputs is presented. A set of necessary and sufficient conditions for this dynamical system to be stable and completely stable are established.