ECE 515: Control System Theory & Design

Course Descriptions:

Feedback control systems emphasizing state space techniques. Basic principles, modeling, analysis, stability, structural properties, optimization, and design to meet specifications.


The current plan is that this course will be taught in person.The situation around Covid-related restrictions on campus can of course change at any moment, and I will keep the class updated of any developments.

Schedule: Mon Wed 11:00am~12:50pm, 2035 Campus Instructional Facility

Prerequisites: MATH 241 or MATH 380; one of MATH 385, MATH 386, MATH 441

Office hours: TBA

Homework TA: TBA

TA Office hours: TBA

Supplementary texts:

  • Michael Greenberg, Advanced Engineering Mathematics, Prentice-Hall

Assignments and grading policy:

Your grades will be based on homework and exams. Details will be explained in class.


  • Week 1: Examples of Linear systems. Lecture Note

  • Week 2: Linear algebra. Linear spaces and transformations. Lecture Note

  • Week 3: Linear algebra. Eigenvalues and eigenvectors. Lecture Note

  • Week 4: Variation-of-constants (VOC) solution formula. Lecture Note

  • Week 5: Properties of fundamental solution matrix and Jordan decomposition. Lecture Note

  • Week 6: Lyapunov stability. Definitions and Lyapunov’s direct method. Lecture Note

  • Week 7: Linear algebra. Inner products and norms. Lecture Note

  • Week 8: Lyapunov theory for linear time invariant systems. Lecture Note

  • Week 9: Linear algebra. Range and null space. Lecture Note

  • Week 10: Controllability and observability. Lecture Note

  • Week 11: Kalman’s controllability and observability decomposition. Lecture Note

  • Week 11: Realization theory. Lecture Note

  • Week 12: Control and observer design. Lecture Note

  • Week 13: Optimal control of linear systems. Lecture Note