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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.

journal of nonlinear sciences and applications./journal of nonlinear sciences and  applications.

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