The aim of the module is to provide a well-rounded exposure to analysis, control and simulation of digital control systems. Theoretical techniques for studying discrete-time linear systems with particular emphasis on the properties and design of sampled-data feedback control systems will be introduced and supported by MATLAB simulations.

By the end of the module you will be able to: 1) Illustrate the issues related to the discretization of continuous-time systems; 2) Devise basic discrete-time control systems using the z-transform and the w-transform; 3) Devise advanced discrete-time control systems using frequency-response methods; 4) Employ the relation between state-space representations and frequency-domain representations; 5) Apply basic principles of optimal control; 6) Devise optimal control laws to solve the linear quadratic regulator problem; 7) Use MATLAB to aid the analysis and design of discrete-time control systems; 8) Relate the introduced ideas and tools with the general theory of dynamical systems.

Aspects of digital signal processing and digital control implementation; z- and w-transforms; Impulse sampling and data hold; The pulse transfer function; Mapping between the s-plane and the z-plane; Stability analysis in the z-plane; Synthesis using indirect and direct design techniques to achieve stability and performance; Analysis and synthesis in state-state; Optimal control and dynamic programming principle; Linear quadratic regulator problem; Models of hybrid systems.