The course deals with the theoretical aspects of linear dynamic systems as they apply to engineering modeling, analysis and design. The mathematical concepts of time and complex frequency domain representation of linear dynamic systems are covered in detail. Furthermore, the theoretical foundations and application of system stability are.
A linear system is a mathematical model of a system based on the use of a linear operator.Linear systems typically exhibit features and properties that are much simpler than the nonlinear case. As a mathematical abstraction or idealization, linear systems find important applications in automatic control theory, signal processing, and telecommunications.
Mathematical fundamentals for analysis of linear systems. Maps and operators in finite and infinite dimensional linear vector spaces, metric spaces, and inner-product spaces. Introduction to representation theory. Eigensystems. Spectral theorems and singular value decomposition. Continuity, convergence and separability. Sturm-Louisville theory.
C.T. Chen, Linear System Theory and Design, 2nd edition, 1995; C.T. Chen, Linear System Theory and Design, 3rd edition, 1998; T.Kailath, Linear Systems, Prentice-Hall, 1980; Grading: Weekly Homework 30% Midterm 30% Final 25% Term project 15%. Prerequisites: Students should have seen topics on linear algebra and matrices. However, a short review.
HW Policy: Homework is assigned and collected. A sample of the problems are graded. Lowest homework grade is dropped. No late homework. References: Linear System Theory and Design, 3 rd edition, C. T. Chen, Oxford, 1998. Linear Systems, Panos Antsaklis and Anthony Michel, McGraw Hill, 1997. Linear Systems, Thomas Kailath, Prentice Hall, 1980.
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Skills homework assignments consist of about 1-10 computational problems per Chapter. These problems are about standard techniques for dealing with linear systems, matrices, and vectors, and are available through and submitted via WeBWorK. Most of these problems were obtained through WeBWorK's National Problem Library. We suggest making these.
Introduction to Linear Control Systems is designed as a standard introduction to linear control systems for all those who one way or another deal with control systems. It can be used as a comprehensive up-to-date textbook for a one-semester 3-credit undergraduate course on linear control systems as the first course on this topic at university.
This session begins our study of systems of differential equations. Systems of DE's have more than one unknown variable. This can happen if you have two or more variables that interact with each other and each influences the other's growth rate. The first thing we'll do is to solve a system of linear DE's using elimination. We do this first.