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

Volume 13, Issue 4, pp 187--195
Publication Date: January 30, 2020 Submission Date: October 20, 2019 Revision Date: November 27, 2019 Accteptance Date: December 10, 2019
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### Authors

Yan Wu - Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA 30460, USA. Sailaja P - Department of Mathematics, Geethanjali Engineering College, Hyderabad, Telangana 501301, India. K. N. Murty - Department of Applied Mathematics, Andhra University, Waltair, AP 530017, India.

### Abstract

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.

### Keywords

• Linear Systems
• time scale dynamical systems
• control systems
• concurrency control

•  93B05
•  93B07
•  93B20
•  93B55
•  93D99

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