In this chapter, st ability and performance for multivariable systems with uncertainty will be considered. Consider a general multivariable system as depicted in Figure 5.1. All signals will in general be vectors, and G() and K(s) will be transfer matrices. d(s) is an output distur- bance signal and n() represents
There are two main limit ations in the use of Hoo theory for compensator design. First, only full complex perturb ations() Cnm can be treated in a non-conservative way in an Ho robust st ability test. Second, robust performance can only be handled in a conservative way even for full complex perturbations since st ability and performance can not be separated in the Hoo structure
Above, analysis for multivariable control systems with respect to nominal and robust st ability as well as nominal and robust performan has been assessed. It was assumed that the spec- ifications for robustness were given in terms of weight matrices Wu(s) and Wu2(s), and that the performance specifications similarly were given by weight matrices Wpi(s) and Wp2()
In order to be able to design a robust compensator to control a given pro cess, it is necessary not only to specify a nominal mo del of the process, but also the model uncert ainty to which the control sy stem has to be robust. The compensator is required to make the output follow variations in the reference signal and to attenuate disturbances. Hence to design the com- pensator
