1.1. What is a Control System
By the term control systems theory, we refer to the discipline that studies the behavior of dynamical systems, physical or artificial, and their control. By system, we refer to a collection of processes or objects, which interact with each other or with the environment and produce a specific outcome. The purpose of control is to manipulate certain parameters of the system in such a way that the outcome of the system will be the desired one. So as can be intuitively understood, dynamic control systems are subject to the axiomatic principle of causality, meaning that a certain action will produce an effect on the system’s behavior.
Control systems refer to a very wide area, covering many disciplines and phenomena. So by this term we do not only refer to systems found in the industry but in any system that operates with the purpose of fulfilling a specific goal. Biology for example is a field that is governed by natural control systems, see for example Liu et al. (2008); Zhang et al. (2012) and the references therein. A characteristic example of a control system found in nature is the human body, which constantly operates by satisfying certain goals such as balance, movement, adjustment of heartbeats according to the body’s functions and more. In medicine as well, automated control systems are found in artificial machinery used for supporting patients (Timms, 2011), for regulating drug dosages in anemic or diabetic patients (Luspay & Grigoriadis, 2016; Parker & Doyle, 2001) and control theory can be applied for formulating strategies for dealing with chronic diseases like HIV or Hepatitis (Craig & Xia, 2005; Moysis, Kafetzis & Politis, 2016; Rivadeneira & Moog, 2012). Other man-made examples used in everyday life is a car that operates according to the driver’s commands, a washing machine, a house’s heating system, an oven, an elevator and other everyday objects. On a larger scale, digital controllers are used in all kinds of industries to control the operating functions of large machinery and keep them functioning under safety regulations, see for example Åström & Kumar (2014); Azar & Serrano (2016a, 2015a, 2015b, 2015c, 2015d, 2014); Azar, Vaidyanathan (2015a, 2014); Azar & Zhu (2015); Bissell (2009); Dorf & Bishop (2011); Ghoudelbourk et al. (2016); Kumar & Daoutidis (1999); Li & Chong (2006); Meghni et al. (2016); Meghni, Dib & Azar (2015); Mekki, Boukhetala & Azar(2015); Nise (2015); Spong (1987); Stroe et al. (2017); Stroe & Andrei (2016); Qin & Badgwell (2003); Zhu & Azar (2015) and the references therein. Even more abstract systems like a nation’s economy are considered control systems, since there is a collection of inputs that the government tries to manipulate, like the amount of taxes and the production of goods to improve the outputs that can be considered the overall salaries or the Gross Domestic Product, see for example the Leontief model for a multisector economy (Campbell, 1982).