On construction of sampling patterns for preserving observability/controllability of linear sampled-data systems

In this paper, we design a new nonequidistant sampling pattern such that the property of controllability and observability of the linear continuous time systems is preserved during the procedure of the sample and zero-order hold operation. The idea behind the strategy comes from Kronecker's theorem and it is proven that new construction is more effective by requiring less number of sampling times which guarantees controllability and observability of sampled-data system in two dimensional space. Moreover, we provide one application in the concept of controllability of the pendulum in two dimensional space and obtain corresponding digital controls which make the corresponding sampled-data system controllable. Finally, the research is extended to different type of sampling patterns which are compared with the constructed sampling pattern separately.