Linear control plants in a resolution space

Abstract

Various facts about causal operators defined on Hilbert spaces and their extensions endowed with time structure were considered in Chapter 3. This provides us with tools permitting to give rich in content settings and analysis of various control problems. This topic is mainly considered in the following part of the book. However, as a first step, it is useful to clarify some fundamental (for the systems theory under consideration) concepts of control plants, linear feedback, stabilizing controller and possible aims of control This chapter considers also relatively simple (non-optimization) problems of linear system theory, usually unified under the general title “the problem of analytical stabilization”. It gives the way of constructing feedbacks for time-invariant control plants. At the end of the chapter we shall return to the robustness problem on the example of time-invariant control plants, described by linear ordinary differential equations with constant coefficients.