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 the Laplace transform, 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 linear ordinary differential equations using the Laplace transform
● Identify vector spaces, their bases, and the role of matrices in mapping between them
● Solve systems of linear equations
● Calculate the eigen-decomposition of matrices
● Utilize matrix representation of linear systems
● Linearize a nonlinear system so that you can model it with our tools
● Understand similarity transformations and diagonalization, and role in state-space models
● Analyze the stability of a linear system
● Understand how linear models lead to controllability and observability
Instructor: Erfan Nozari (erfan.nozari@ucr.edu)
TA: Qiyang Sun (qsun026@ucr.edu)
Lecture Times & Location: Tuesdays & Thursdays, 11:00am - 12:20pm Pacific Time; Zoom link announced on iLearn
Discussion Times: Mondays, 2:00 - 2:50pm and Fridays, 1:00 - 1:50pm Pacific Time; Zoom link announced on iLearn (different from class link, hosted by the TA)
Instructor Office Hours: Mondays, 11:00am - 12:00pm & Thursdays, 10:00 - 11:00am 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.
Optional (but highly recommended) Moodle course on complex numbers and linear algebra: https://linearalgebraintro.moodlecloud.com/. Note that you can go through the lessons and answer the exercises as many time as you want, but will get partial grades if you get the right answer to any exercise on the 2nd or later tries.
Lecture Notes:
Lecture 0: Preliminaries
Lecture 1: Linear Algebra
Lecture 2: Linear Systems
Lecture 3: Stability, Controllability & Observability
Grading: midterm & final: 15%/65% or 40%/40% (whichever helps you), homeworks: 20% + 7% extra, Moodle scores: 5% extra, course evaluations: 3% extra
Homeworks: 8 sets (6 sets + 2 sets extra grade), about one per week; due on Thursdays at midnight Pacific Time; posted at least one weak before on this page and on iLearn; submitted via iLearn
Homework 7
Syllabus (tentative):
Weeks 0 & 1 (10/1, 10/6, 10/8): Preliminaries (complex numbers, differential equations, Laplace transform)
Weeks 2 - 5 (10/13, 10/15, 10/20, 10/22, 10/27, 10/29, 11/3): Linear algebra
Midterm: 11/5, during normal class time
Week 6 (11/10, 11/12): Introduction to signals & systems, state space equations, electromechanical systems
Weeks 7 & 8a (11/17, 11/19, 11/24): Properties of linear systems
Week 9 (12/1, 12/3): Stability
Week 10 (12/8, 12/10): Controllability & observability
Final: Monday, December 14, 8:00 - 11:00 am Pacific time.