With the fundamental patterned system properties established in the previous chapter, the framework is in place to examine more complex controller synthesis problems. We consider a variety of classic synthesis questions for patterned systems, including the Measurement Feedback Problem, the Disturbance Decoupling Problem, the Output Stabilization Problem, and the Restricted Regulator Problem. In each case the objective is to determine conditions for the existence of a patterned feedback solution. This is a more restrictive challenge than the general feedback problem. Remarkably, it emerges that the necessary and sufficient conditions for the existence of any feedback solving these synthesis problems are also necessary and sufficient for a patterned feedback.
For each synthesis problem, we first review the established results for general systems and then present the equivalent patterned problem. This facilitates comparison and will hopefully prove helpful for those readers who are not familiar with some of the original geometric results. The material in this chapter largely follows the presentation of Wonham , although we attempt to show more explicitly the relationship between subspaces and matrices in some areas.
KeywordsState Feedback Control Synthesis Output Stabilization Synthesis Problem Measurement Feedback
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