This is an introductory course at the undergraduate level to systems and controls. We will focus on the linear systems, both because of their simplicity, and due to their ubiquitous use in different applications. We will briefly review some preliminaries about differential equations and complex numbers, before covering the fundamentals of linear algebra as the basis of linear systems theory. Then, we will move on with the main topics of the course, including state space linear system models, their solutions and properties, linearization of nonlinear systems, stability, controllability and observability. Prerequisite: EE 001A, EE 01LA, ME 018B.
Course Objective: by the end of this course, you should be able to
● Solve ordinary differential equations using MATLAB
● Identify linearly dependent and independent set of vectors in Euclidean space
● Solve systems of linear equations
● Calculate the eigen-decomposition of matrices
● Utilize matrix representation of linear systems
● Linearize a nonlinear system around an equilibrium point
● Analyze the stability of a linear system
● Understand the controllability and observability of a linear system
● Design static linear state feedback for controllable systems
Instructor: Erfan Nozari (erfan.nozari@ucr.edu)
TA: Kyungjoon (Harry) Lee (klee449@ucr.edu)
Lecture Times & Location: M \& W, 2:00 - 3:20pm Pacific Time; via Zoom (link announced on iLearn)
Discussion Times: Mondays, 1:00 - 1:50pm and Fridays, 3:00 - 3:50pm Pacific Time; first week via Zoom (link announced on iLearn -- different from class link, hosted by the TA)
Instructor Office Hours: Thursdays, 2:00 - 3:00pm Pacific Time; same Zoom link as class. Other times can be scheduled via email.
Source material: Instructor's lecture notes (updated regularly, even retrospectively, so always check to make sure you have the latest version).
Optional textbook: C. T. Chen, "Linear System Theory and Design", Oxford University Press.
Lecture Notes:
Lecture 0: Preliminaries
Lecture 1: Linear Algebra
Lecture 2: Linear Systems
Lecture 3 - Stability, Controllability & State Feedback
Grading: midterm & final: 20%/60% or 40%/40% (whichever helps you), homeworks: 20% + 7% extra, course evaluations: 3% extra
Homeworks: 8 sets (6 sets + 2 sets extra grade), about one per week; due on Mondays at 2:00pm; posted at least one weak before on iLearn; submitted via iLearn
Schedule (tentative):
Weeks 1 (9/27, 9/29): Preliminaries (complex numbers, differential equations)
Weeks 2 - 5 (10/4, 10/6, 10/11, 10/13, 10/18, 10/20, 10/25, 10/27): Linear algebra
Week 6 (11/1): Introduction to signals & systems, state space equations, models of mechanical systems
Midterm: 11/3, during normal class time
Weeks 7 & 8 (11/8, 11/10, 11/15, 11/17): Properties of linear systems
Week 9 (11/22, 11/24): Stability
Week 10 (11/29, 12/1): Controllability, observability, and Feedback Control
Final: Tuesday, December 7, 7:00 - 10:00 p.m. Pacific time (via Zoom)