CDS 131: Linear System Theory

I developed and taught 16 lectures of the CDS core PhD course on linear system theory. This course focuses on the analysis and control of linear control systems (e.g. control systems of the form \(\dot x(t) = Ax(t) + Bu(t)\), etc.). We developed from scratch the fundamental concepts from dynamical systems, starting from existence and uniqueness of solutions to linear systems systems. We then studied state transition matrices, transfer functions, stability theory, convex controller synthesis from Lyapunov equations. Following this, we examined controllability & observability, and state & output feedback, concluding the classical linear systems material with a study of optimal control & the Youla parameterization. As opposed to emphasizing hand calculations, we focused primaily on developing deeper theoretical insights and leveraging tools from optimization in control design.

I also developed weekly course assignments reinforcing the theory we covered in lecture, as well as a set of comprehensive lecture notes on linear system theory. Further, I recorded a large number of lectures, which are freely available online.

I was fortunate to receive the Caltech graduate Excellence in Teaching award for my work on the course.

Course Website

Recorded Lectures