CSD approach to stabilization control and H₂ optimal control

For a control system under investigation, an important design objective is to find a controller such that the closed-loop system satisfies a set of desired specifications. Furthermore, it is desirable to characterize all such controllers which achieve the required specifications. To accomplish this task, the required specifications can be first formulated into an adequate performance index, and then one can minimize the index to obtain sought controllers. This chapter presents a unified approach for solving a fairly general class of control synthesis problems by employing chain scattering-matrix descriptions and coprime factorizations. In particular, robust stabilization problems and the optimal H₂ control will be discussed in this chapter, respectively. The H_∞ (sub)optimal control problem can also be solved along the same approach which will be presented in the next chapter.