Afterwards the student is able to:
- formulate linear differential equations with constant coefficients and find corresponding solutions using matrix exponentials;
- establish for a linear system, whether it is controllable, observable, stabilisable and/or detectable;
- design an observer and stabilising controller based on a state description of the system;
- apply the techniques of this course to an application.
The course starts with a brief introduction to differential equations. The focus will be on linear differential equations with constant coefficients. The exponential matrix eAt is introduced formally for diagonalizable matrices A and it is briefly mentioned what the exponential matrix looks like, in general, on the basis of the Jordan form. (However, we do not compute Jordan forms.) It is then connected to the solution of a system of linear differential equations. Next, the focus is on dynamical systems with inputs and outputs, especially linear systems and their state representations. An important problem is the extent to which the dynamical behaviour can be controlled by the choice of input. In contrast to standard ODEs, we may be able to turn ODEs with unstable behaviour into ODEs with stable behaviour by carefully choosing the input. For this type of analysis, we need the notions of controllability, detectability and observability. This will require notions from Linear Structures. We design observers to estimate the state of a system, and we design dynamical stabilising controllers using static state feedback in combination with observers. |
Project assignment (20%)
Written exam (80%)