Multivariable control system also known as MIMO (Multi-Input and Multi-Output) system, is one of the most important branches of control engineering. Due to its applications in various industries, has been attractive for researchers in recent decades, and hundreds of articles and dozens of books have been published about analysis and design controllers for them. for instance, we can name the following industries: Power Plants, Chemical Industries, Food Industries, Automobile Manufacturing, Aerospace Systems, robotics, etc.
The main problem in multivariable systems is the problem of “Interaction”, which decreases the performance of the systems and in some cases causes the Instability of the closed loop. In MIMO systems, changing the control parameter of one loop can affect the behavior of several other variables in other control loops.

In this course, we will first introduce how to analyze Multivariable control systems, then we will start to design the controller. The existing methods for analyzing and designing MIMO control systems are generalizations of the methods used in Linear control and Modern control systems.

Prerequisite: Linear Control, Modern Control, MATLAB and Simulink


Dr Ali Khaki Sedigh

Dr. Ali Khaki-Sedigh

Department of Electrical Engineering, Control Systems
Member of APAC research group
K. N. Toosi University of Science and Technology

  • Introduction to MIMO control systems
  • MIMO linear systems representation
  • Zeros and poles in MIMO systems
  • Analysis and design of MIMO control systems in state-space
  • Stability and limitations on the performance of MIMO systems
  • Analysis of stability and performance of uncertain MIMO systems
  • Classic topics of designing MIMO control systems
  • PI controller of MIMO systems
  • Nonsquare MIMO systems
  1. Multivariable Feedback Control, S. Skogestad, I. Postlethwaite, Wiley, 2005.
  2. Linear Robust Control, M. Green, D J N Limebeer, Prentice-Hall, 1995.
  3. Multivariable Control System Design Techniques, G. F. Bryant, L. Yeung, Wiley 1996.
  4. Linear Control System Analysis and Design, J J Dazzo, C H Houpis, McGraw-Hill, 1988.
  5. Multivariable System Theory and Design, R V Patel, N Munro, Pergammon Press, 1982.
  6. Multivariable Feedback Design, J M Maciejowski, Wesley,1989.
  7. Control Configuration Selection in Multivariable Plants, A. KhakiSedigh, B. Moaveni, Springer Verlag, 2009.
1Introduction257 KBDirect Link
2Multivariable System Representation93 KBDirect Link
3Poles and Zeros906 KBDirect Link
4State-Space Analysis and Design839 KBDirect Link
5State-Feedback Decoupling1.29 MBDirect Link
6Stability and Limitations1.25 MBDirect Link
7Robust Stability and Performance1 MBDirect Link
8Classic Design2.21 MBDirect Link
9PI Controller1 MBDirect Link