Ayrık modellerin kontrol edilebilirliği ve gözlenebilirliği üzerine bazı sonuçlar

In this thesis, we obtain novel results on controllability and observability of some discrete models. The thesis consantrates on two main parts. In the first part, some topological results are obtained and investigated by associating their connection in discrete control systems. In the second part, a novel sampling pattern is constructed and added to the literature related to preserving the property of controllability/observability of sampled-data control systems. Firstly, we start with examining some special type of sequences in which each candidate is a polynomial with its coefficients are of integers taken from a discrete set. Here, we contribute facts on behaviour of elements of some constructed sets related to the context, some of which are general version of recent works in the literature. As one application of the theory, we propose a one dimensional controllability problem of a convex polyhedra with finite number of controls acting on the system and prove that the reachable set of the discrete model is dense in the set of real numbers under the suitable finite control set. Secondly, 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. Moreover, we provide one application in the concept of controllability of the pendulum in two dimensional setting and obtain corresponding digital controls which make the corresponding sampled-data system controllable.