# Systems and Control Theory

## Overview

Mathematical Systems and Control Theory considers dynamical systems which can be influenced from the outside by a control input, so called control systems. While control theory puts the emphasis on computing a control input for obtaining a given control goal (e.g., reach a given target in a minimal amount of time), systems theory is focused on the analysis of the system's behaviour, either for a given control or for all possible control inputs (e.g., whether a given target is reachable, at all). The important feature in both cases is that the changes of the system state in time is explicitly taken into account, both when selecting the control input, which itself varies with time, and also for defining the control objective. The two most important control concepts are*open loop*control, in which a time varying control is computed in advance for all future time instants, and

*closed loop*or

*feedback*control, in which the control input depends (directly or via measured output values) on the current state of the system.