Key Words--~=-optimal control; robust control.
Abstract--The paper presents a tutorial exposition of
~=-optimal regulation theory, emphasizing the relevance of
the mixed sensitivity problem for robust control system
THE INVESTIGATION OF ~®-optimization of control
systems began in 1979 with a conference paper by
Zames (1979), who considered the minimization of
the oo-norm of the sensitivity function of a
single-input-single-output linear feedback system.
The work dealt with some of the basic questions of
"classical" control theory, and immediately caught a
great deal of attention. It was soon extended to more
general problems, in particular when it was recognized
that the approach allows dealing with robustness far
more directly than other optimization methods.
The name "~K~-optimization" is somewhat unfortunate.
~® is one member of the family of spaces
introduced by the mathematician Hardy. It is the
space of functions on the complex plane that are
analytic and bounded in the right-half plane. The
space plays an important role in the deeper
mathematics needed to solve K-optimal control
This paper presents a tutorial exposition of the
subject. The emphasis is on explaining the relevance
of K-optimization for control engineering. The paper
presents few new results, and does not at all do justice
to the extensive theoretical and mathematical
literature on the subject. The presentation is limited
to single-input-single-output (SISO) control systems.
Many of the arguments carry over to the multi-input-
* Received 6 February 1992; revised 6 July 1992; received
in final form 23 August 1992. The original version of this
paper was presented at the IFAC Symposium on Design
Methods of Control Systems which was held in Ziirich,