This course will introduce students to the analysis and design of linear multivariable (Multiple Input Multiple-Output (MIMO)) control systems in continuous-time. The course focuses on the analysis and design of control systems in the state-space and their applications to electrical, hydraulic, and mechanical systems. Controllability and observability. Lyapunov Stability. Description of disturbances and their effects. Emphasis is given on the controller synthesis using state-feedback control, the linear quadratic (LQ) theory and the separation theorem (separation of control and estimation problems). Design of observers (Luenberger) and optimal state estimators (Kalman filters). Linear-quadratic-gaussian (LQG) control. The course will also prepare the students for further study in control theory (robust control, adaptive control, system identification and model predictive control).

1. Introduction to linear multivariable control systems (SISO/MIMO limitations) 
2. Mathematical modelling in state-space domain for multivariable systems
   a. Time response multivariable systems
   b. Controllability, observability, detectability, stabilizability and minimal realizations
   c. Poles, eigenvalues and stability of multivariable linear systems
3. Lyapunov stability for linear and nonlinear systems
4. State-feedback control (pole placement) and state observers (Luenberger)
5. Optimal state-feedback control (Linear-Quadratic Control) and optimal state estimation (Kalman Filters)
6. The H2 optimal control problem
7. The H∞ control problem and robustness

Suggested Literature :

• Åström, K.J., Murray, R. M., “Feedback Systems: An Introduction for Scientists and Engineers,” 2nd Edition, Princeton University Press, 2021.
• Skogestad, S., Postlethwaite, I., “Multivariable Feedback Control, Analysis and Design,” 2nd Edition. John Wiley and
  Sons, 2005.
• Franklin, G. F., Powell, J. D., Emami-Naeini, A., “Feedback Control of Dynamic Systems,” 8th Edition, Pearson, 2019.
• Dorf R.C., Bishop R.H., “Modern Control Systems,” 13th Edition, Prentice Hall, 2016.
• Ogata, K., “Modern Control Engineering,” 5th Edition, Prentice-Hall, 2011.
• Zhou, K., Doyle, J. C., “Essentials of Robust Control,” Prentice Hall, 1999.
• Antsaklis, P. J., Michel, A., N., “A Linear Systems Primer,” Birkhauser, Boston, 2007.
• D’Azzo J.J, Houpis C.H., “Linear Control System Analysis & Design”, 4th Ed., McGraw-Hill, 1988.
• Chen, C.T., “Linear System Theory and Design,” 4th Edition, Oxford University Press, 2012.
• Simon, D., “Optimal State Estimation,” John Wiley & Sons, 2006.
• Anderson, B.D.O., Moore, J.B., “Optimal Filtering,” Dover Publications, 2005.
• Stengel, R.F. “Optimal Control and Estimation”, Dover Publications, 1994.
• Rossiter, J.A., “Model Based Predictive Control: A Practical Approach,” CRC Press, 2005.
• Camacho E.F., Bordons, C., “Model Predictive Control”, Springer, 1999.
• Kouvaritakis B., Cannon, M., “Non-Linear Predictive Control: Theory & Practice”, IEE Publishing, 2001.
• Maciejowski, J., “Predictive Control with Constraints”, Pearson Education POD, 2002.
• Burl, J.B. “Linear Optimal Control: H2 and H∞ Methods,” Addison-Wesley, Menlo Park, CA, 1999.

Related Academic Journals:

• Automatica
• Control Engineering Practice
• IEEE Transactions on Automatic Control
• IEEE Transactions on Control of Network Systems
• IEEE Transactions on Control Systems Technology
• IET Control Theory and Applications
• International Journal of Control
• International Journal of Robust and Nonlinear Control
•  Systems and Control Letters

Greek or English

 Lectures and coursework