OPTIMAL CONTROL APPLICATIONS AND METHODS Optim. Control Appl. Meth., 2004; 25:51–66 (DOI: 10.1002/oca.738) Switching between multivariable controllers Henrik Niemann 1,n,y , Jakob Stoustrup 2,z and Rune B. Abrahamsen 3 1 Ørsted DTU, Automation, Technical University of Denmark, Building 326, Lyngby DK-2800, Denmark 2 Department of Control Engineering, Aalborg University, Fr. Bajers Vej 7C, Aalborg DK-9220, Denmark 3 Space Systems Division, Rovsing A/S, Dyreg ( ardsvej 2, Skovlunde DK-2740, Denmark SUMMARY A concept for implementation of multivariable controllers is presented in this paper. The concept is based on the Youla–Jabr–Bongiorno–Kucera (YJBK) parameterization of all stabilizing controllers. Using this scheme for implementation of multivariable controllers, it is shown how it is possible to smoothly switch between multivariable controllers with guaranteed closed-loop stability. This includes also the case where one or more controllers are unstable. The concept for smooth on-line changes of multivariable controllers based on the YJBK architecture can also handle the start-up and shut down of multivariable systems. Furthermore, the start-up of unstable multivariable controllers can be handled as well. Finally, implementation of (unstable) controllers as a stable Q parameter in a Q-parameterized controller can also be achieved. Copyright # 2004 John Wiley & Sons, Ltd. KEY WORDS: multivariable controllers; parameterization; switching; controller implementation; stabiliz- ing controllers 1. MOTIVATION}AN EXAMPLE Some aspects of stability in connection with implementation of controllers for multivariable systems are considered in this paper. This includes both implementation of unstable controllers as well as on-line change between a number of controllers. Even for stable systems, most (post-) modern control techniques based on various optimization techniques, such as H 2 ; H 1 ; L 1 =‘ 1 norm based or m optimization-based designs tend to provide unstable controllers. The industrial use of unstable controllers has been limited. This is unfortunate, considering that for some plants, no stable controller will achieve optimality (in a mixed sensitivity sense). Moreover, for some plants, no stable controller will robustly stabilize the system. Finally, for Received 25 November 2002 Revised 12 December 2003 Copyright # 2004 John Wiley & Sons, Ltd. y E-mail: hhn@oersted.dtu.dk n Correspondence to: Prof. Henrik Niemann, Ørsted DTU, Automation, Technical University of Denmark, Building 326, DK-2800 Lyngby, Denmark. z E-mail: jakob@.control.aau.dk