Introduction to Systems

Abstract

This chapter begins with a brief overview of the study of systems, in Sect. 1.1, which is based on four steps: modeling, setting up mathematical equations, analysis, and design. Section 1.2 introduces the second step of the study of systems, setting up mathematical equations to describe the system, referring to the standard forms of input-output and state-variable descriptions of systems. Section 1.3 introduces the principal concept of component analysis of linear systems based on the theory of controllability, observability, and identifiability of systems with regard to their mathematical forms of notation, showing what can be achieved under their assumptions. Section 1.4 introduces the analytical solutions of linear systems by analyzing their behavior and/or composite structure to examine the system response to an input demand. Section 1.5 refers to the approach determining the steady-state error of systems, an analysis method which defines the difference between input and output of a system in the limit as time goes to infinity. Section 1.6 provides a case study on the implications of the concept of system stability analysis. Section 1.7 contains comprehensive questions from the introduction to systems topics, and followed by references and suggestions for further reading.