State space methods (single-input single-output)

• State space models and transfer functions, state feedback 
• Coordinate basis, similarity transformations 
• Solutions of state equations, matrix exponentials, Caley-Hamilton Theorem
• Controllability and pole placement 
• State estimation, observability, Kalman decomposition 
• Observer-based state feedback control, reference tracking 
• Transmission zeros
• Optimal pole placement, symmetric root locus 
Multi-input multi-output systems
• Transfer function matrices, state space models of multivariable systems, Gilbert realization 
• Poles and zeros of multivariable systems, minimal realization 
• Closed-loop stability
• Pole placement for multivariable systems, LQR design, Kalman filter 

Digital Control
• Discrete-time systems: difference equations and z-transform 
• Discrete-time state space models, sampled data systems, poles and zeros 
• Frequency response of sampled data systems, choice of sampling rate 

System identification and model order reduction 
• Least squares estimation, ARX models, persistent excitation 
• Identification of state space models, subspace identification 
• Balanced realization and model order reduction 

Case study
• Modelling and multivariable control of a process evaporator using Matlab and Simulink 
Software tools
• Matlab/Simulink