This module aims to introduce you to state-space methods for the analysis and design of control systems. You will learn how to obtain state-space models from transfer functions and vice versa. You will assess the stability properties of dynamical systems and structural properties such as reachability and observability. Finally, you will design feedback controllers in a systematic way to modify the behaviour of the system.

Upon successful completion of this module, you will be able to:
1. Construct models of dynamical systems using differential and difference equations
2. Compute a state-space representation from a given transfer function and vice versa, and quantify difference between the two representations
3. Assess stability properties of dynamical systems and structural properties
4. Devise feedback controllers in a systematic way to modify the behaviour of dynamical systems
5. Assess a priori what behaviour can and cannot be achieved in a dynamical system
6. Devise, implement and validate a linear regulator

Abstract dynamical systems;
Differential and difference equations;
State space models;
Lyapunov stability;
Structural properties (controllability and observability);
Kalman decomposition;
Pole placement via state feedback and dynamic output feedback;
Observer design.