ABSTRACT
The author recommends the basic notions and the basic discoveries of this book (system regimes, desired regime, nominal control, the system full transfer function matrix F (s), linear tracking control synthesis by using F (s)) to become the parts of the …rst course on linear control time-invariant continuous-time systems. Other issues and results (tracking properties, trackability properties, the conditions for them, Lyapunov tracking control synthesis and natural tracking control synthesis) should enrich and re…ne the content of the advanced linear control systems courses. Therefore, the author hopes the twenty-…rst century linear control sys-
tems courses:
will incorporate both
- the system full (complete) transfer function matrix F (s) as the basic system dynamic characteristic in the complex domain, as well as its applications to various issues of control systems, e.g., to the system complete response, pole-zero cancellation, the stability theory, and to the optimal control theory, which are the basic issues of the dynamic systems theory in general and of the control theory in particular, and
- the tracking and trackability theories as the fundamentals of the control theory and of the control engineering, which express the primary control goal;
will re…ne the study in the complex domain of the qualitative system properties by using the system full transfer function matrix F (s) instead of the system transfer function matrix G(s);
will devote more attention to the basic system phenomena such as system desired regimes and the nominal control ;
and
will pay attention to the di¤ erences between
- the transfer function matrix realization and the system realization that reduces to the full transfer function matrix realization,
and - the irreducible complex rational matrix functions and the degener-
ate complex rational matrix functions. The accompanying book [148] discovers and proves the following:
The incompetence of the system transfer function matrix G(s) for Lyapunov stability tests. Only the system full transfer function matrix F (s); or at least its adequate submatrix that is the submatrix related to the internal initial conditions, is competent for Lyapunov stability tests.
