Partial Interconnection Issues

In this chapter we shall continue the development we started in the previous chapter. Instead of full interconnection, we will now deal with the case of partial interconnection. We will start with reviewing the notions of implementability and regular implementability. Next we will deal with the problems of pole placement and stabilization by partial regular interconnection. We will set up algorithms to compute regular controllers for a given plant that achieve pole placement or stabilization. Next, we show how to implement these algorithms in MATLAB. An important part of this chapter deals with the problem of parametrizing (for the partial interconnection case) all controllers that regularly implement a given desired behavior. We will establish such parametrization, first under certain observability assumptions, and afterwards also in the general case. Also for this parametrization problem, we will give numerical algorithms. Finally, we will address the problem of parametrizing for a given plant, all controllers that stabilize the given plant by regular partial interconnection. Also for this problem we give the corresponding MATLAB codes and some examples runned with comments. We conclude the chapter with a summary.