Modern Control System Theory and Design, 2nd Edition

8.13.  LINEAR ALGEBRAIC ASPECTS OF CONTROL-SYSTEM DESIGN COMPUTATIONS [21–24]

The fundamental problems of linear control-system theory were reconsidered at the end of the 1960s and the beginning of the 1970s. The algebraic characteristics of the control-system problems were reestablished and have resulted in a better understanding of the foundations of linear control-system theory.

This section focuses on the interplay between some recent results and methodologies in numerical linear algebra and their application to problems arising in control systems. Let us reconsider the phase-variable canonical form representation of a control system:

Figure 8.35  Optimal sensitivity frequency characteristic as a function of T.

We can represent this canonical form representation in terms of its frequency response by using Eqs. (8.10) and (8.18):

The problem of computing C(s)/R(s), or C(jω/R(jω), from knowledge of K, P, b, L, and h, efficiently is a practical problem of great interest. Reference 23 presents an efficient and generally applicable algorithm to solve this problem. The approach recommended ...