The Mathematical Theory of Systems and Control (MTSC) is a relatively new field of applied mathematics, whose age does not exceed 50-60 years, sharing common characteristics with Mathematical Physics but also having many significant differences.

The subject of MTSC is the study of the mathematical structure and behavior of systems that occur in nature or are human inventions. Through this study, controllers of systems are analyzed and synthesized with the aim of controlling their behavior, based on findings that stem from the mathematical framework.

In contrast to the scientific researcher in the Natural Sciences, the theoretical Systems and Control researcher cannot rely solely on experimental results. The mathematical rules governing the behavior of systems and determining the means of controlling that behavior are achieved through a mathematical analysis, whose foundations are axiomatic.

The subtitle: Modern Control Theory of this second volume of the Introduction to the Mathematical Theory of Signals, Systems, and Control (IMTSSC) refers to the method of formulating, investigating, and solving problems of MTSC, based on the use of mathematical models of systems, known in the literature as state space models.

This branch of applied Mathematics is known as Modern Control Theory, as research activity in this area began after the 1940s. The theory and practice of automatic control of systems is continually evolving, primarily through the research efforts of mathematicians and engineers in the U.S., the former Soviet Union, and the United Kingdom. The state space has developed into a dynamic and rapidly growing research area in applied Mathematics.

The state space has achieved great success in applications and provides a very useful and practical mathematical tool for the description and addressing of analysis and synthesis problems of automatic control systems in the time domain.