The four block problem for distributed systems
Tannenbaum, Allen R.
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A study is made of the singular values of the four-block operator, which appears naturally in many H∞ control problems. Following the framework of the monograph of B.A. Francis (1987), almost all such robust design problems can be formulated in terms of the spectral properties of such an operator. This includes the problems of sensitivity and mixed-sensitivity minimization, model matching, and certain tracking problems. The authors' techniques give the optimal solution to this problem, which is valid for a large class of distributed systems.