Control theory for the discrete systems

CONTROL THEORY FOR THE DISCRETE SYSTEMS Burcum ÖZDEMİR Department of Mathematics, M.Sc. Thesis, 2002 Thesis Supervisor: Prof. Dr. Ömer AKIN SUMMARY The aim of this thesis is to introduce control theory, speacialy to mathematicians, which has been used in applied mathematics and some branches of engineering. Therefore all fundamental knowledge related to control theory in details will be presented here. In this work, notions related to linear algebra, systems of finite differences and systems of differential equations are used as the basis of this study. One of the aims of this thesis to give fundamental knowledge to understand articles and do works related to control theory. Under the aims mentioned above, this thesis consists of four parts. In the first part, we take attention to basic notions and properties used in the thesis. In the second part, the controllability, reachability, duality and some relations among them for the continious systems are examined. In the third part, which is the main part of the thesis, we examined the control theory for the discrete systems, give theorems (with proofs) and some examples. In the fourth and the last part, we give some applications of the discrete control theory by using the software of MATLAB. Keywords: Control, Controllability, Control Systems, Discrete Systems.