Linear control Theory is the most mature and most basic composition branch in the system and control theory, which is the cornerstone of modern control theory. Other branches of the system and control theory are affected and driven by the concepts, methods and results of linear control theory varying degrees. The research object of linear system theory is a linear system, which is an idealized model of the actual system, usually described in linear differential equations and differential equations. The system is a whole with a certain component of several components of interrelation and interactions. The system can have a completely different attributes such as engineering systems, biological systems, economic systems, social systems, etc. However, in the system theory, the physical or social meaning of the specific system is often taken into an abstract system into a general system, which helps reveal the general characteristics of the system. The most basic feature of the system is that its integrity, the behavior and performance of the system is determined by its overall, and the system can have functions in which their components are different, and there are two different components but their associations and respective relationships are different. The system can present very different behaviors and functions. In the system and control theory, we will mainly study dynamic systems, usually referred to as kinetic systems. Dynamic systems are often characterized by a set of differential equations or differential equations, and a strict and quantitative mathematical description can be given to the motion of the system and various properties. When describing the mathematical equation of the dynamic system has a linear property, the corresponding system is a linear system. Linear systems are the easiest and most developed dynamic systems. Strictly speaking, all actual systems are nonlinear, and the real linear system does not exist in the real world. However, a large part of the actual system, some of its main relationship characteristics, can fully accurately use a linear system to approximately represent a linear system within a certain range. Also, the difference between the actual system and the idealized linear system is negligible for the extent to which the problem has been considered, and it can be ignored. Therefore, in this sense, the linear system or linear system is in a large amount, which is the actual background of the linear system. Briefly, the linear system theory mainly studies the motion law of the linear system state and the possibility of changing this movement law, establish and reveal the determination and quantitative relationship between system structure, parameters, behavioral and performance. In the process of researching the system, establishing a reasonable system mathematical model is the primary premise, for linear systems, common models have time domain models and frequency domain models, and the time domain model is more intuitive, and the frequency domain model is one more Powerful tools, the basic pathways established are generally analyzed and experimental methods. The mathematical model provides the possibility of solving the problem. On this basis, it is also necessary to add a control portion to the system to achieve the desired performance, which can first add some links in the mathematical model, and then implement it in actual. The classic linear control theory is a major tool in the 50-year industry in the 50-year industry. Later, some new mathematics tools were used, and advanced computer technology was also used, which promoted the further development of linear system theory and widely used in actual. In the 1950s, the classic linear system theory has developed maturity and complete, and has been applied in many engineering and technical fields. The mathematical foundation is Laplas transform, and the model is the transfer function, analysis and integrated approach is the frequency response method. However, it has significant limitations, highlighting is difficult to solve the multi-input-multi-output system, and difficult to reveal the deeper characteristics of the system. Under the promotion of aerospace technology in the 1950s, the linear system theory has started the transition from the classic to modern phases before and after 1960, and one of its important signs is to introduce state space method to the system and in the REKALMAN. Control theory. On this basis, Karman further proposes the important conceptual concepts that can control and observe the structural characteristics of the characteristic system, which has proven that this is the two most basic concepts in the linear system theory.
The analysis and integrated method of linear system based on state space method is often referred to as modern linear system theory. Since the mid-1960s, linear system theory has not only research content or research methods, but also a series of new development. This kind of geometric theory of the structure and characteristics of the linear system appears from the perspective of geometric method, and an algebraic theory of the abstract algebra. The multivariate frequency domain theory developed on the basis of promoting classical frequency is also emerged. At the same time, with the development and popularization of computer technology, linear system analysis and computational problems, and use of computer-to-analyze and assist design using computers, it has also been widely studied.
