About the Course:

MAE 270A is a graduate course on linear systems. Specific topics included state-space description of linear time-invariant (LTI) and time-varying (LTV) systems in continuous and discrete time. Linear algebra concepts such as eigenvalues and eigenvectors, singular values, Cayley/Hamilton theorem, Jordan form; solution of state equations; stability, controllability, observability, realizability, and minimality.

Abstract:

The goal of this project was to identify and verify the minimal state-space model for a two-input, two-output system. The initial information includes recorded pulse response data as well as white noise response data. We determined the physical components of the system with eigenvalue and transmission zero analysis. We verified the model using a norm analysis, which additionally provided insight on the robustness of the derived model. The minimal model has state dimension seven, and the physical system is composed of two oscillators, two low-pass filters, and one high-pass filter. We used a norm analysis of both the H-2 norm and the H-infinity norm of to cross-validate the derived model and quantify its robustness.