Copyright © IFAC Robust Control Design Milan, Italy, 2003 ELSEVIER IFAC PUBLICATIONS www.elsevier.com/locate/ifac SOLVING WEIGHTED MIXED SENSITIVITY H _ PROBLEM BY DECENTRALIZED CONTROL FEEDBACK VIA MODIFYING WEIGHTING FUNCTIONS AND USING DESCRIPTOR SYSTEM REPRESENTATION Batool Labibi", Ali Khaki Sedigh', Parviz Jabedar Maralani", and Boris Lohmann'" • K.N Toosi University of Technology, Tehran, Iran •• University ofTehran. Tehran, Iran ••• University of Bremen, Bremen, Germany labibi@eeld.knlu.ac.ir. sedigh@eetd.kntu.ac.ir, pjabedar@ut.ac.ir, bl@iat.uni-bremen.de Abstract: This paper considers the problem of achieving stability and certain H_ performance for a large-scale system by a decentralised control feedback law. For a given large-scale system an equivalent descriptor system in input-output decentralised form is defined. For solving the performance problem which is formulated as the standard weighted mixed sensitivity H _ problem, modification of the original weighting functions is proposed. Some sufficient conditions are proposed when satisfied the overall stability and performance of the large-scale system is guaranteed. Copyright © 2003 IFAC Keywords: Large-scale system, H _ control, Decentralised control, Weighted mixed sensitivity H _ problem, Weighting function, Input decentralised form, Input-output decentralised form, Descriptor system. I. INTRODUCTION The problem of designing decentralised control for large-scale interconnected systems has attracted a great amount of interest in recent years. One reason is that the interconnected system can be decomposed into several lower-order subsystems and therefore the design and implementation of each subsystem can proceed independently (Jamshidi, 1997; Siljak, 1991 ). Mixed sensItIvIty is the name given to transfer function shaping problems in which the sensitivity 19 function is shaped along with one or more other closed-loop transfer functions such as KS or the complementary sensitivity function (Maciejowski, 1989; Skogestad, 1996). In this paper a method for solving the mixed sensitivity H _ problem by a decentralised control is proposed. It is shown how by appropriately modifying the weighting functions in original mixed sensitivity problem the overall stability and performance can be achieved by a decentralised feedback control.