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
● 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: Fahimeh Arab (farab002@ucr.edu)
Lecture Times & Location: MW, 2:00 - 3:20pm; via Zoom (link announced on Canvas)
Discussion Times (tentatively in-person): Mondays, 1:00 - 1:50pm in WCH 143 and Fridays, 3:00 - 3:50pm in Sproul Hall 2340
Instructor Office Hours: TBD.
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 30%/50% (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 Canvas; submitted via Gradescope
Tentative Schedule:
Weeks 1 (9/26, 9/28): Preliminaries (complex numbers, differential equations)
Weeks 2 - 6a (10/3, 10/5, 10/10, 10/12, 10/17, 10/19, 10/24, 10/26, 10/31): Linear algebra
Week 6b (11/2): MIDTERM EXAM: from the material taught in Weeks 1-5, held during normal class time
Week 7a (11/7): Linear algebra
Week 7b-9a (11/9, 11/14, 11/16, 11/21): Linear Systems
Week 9b (11/23): Stability
Week 10 (11/28, 11/30): Controllability, observability, and Feedback Control
FINAL EXAM: Monday, December 5, 3:00 p.m. - 6:00 p.m.