brilliant-ember / linear_systems_notes Goto Github PK

A set of helper functions and code that will help solve linear systems problems

note the ipynb files are more complete than the .py files.

This repo will help you do the following and more:

1. State transition matrix (both continuous time and discrete)
2. Homogenous response (aka free response or zero input response) of a state space model both continuous and discrete
3. Forced response (aka zero state response) of a state space model
4. Output response of a state space model
5. Determine and Contralabiltiy and Observability of a system, and find the contralabilty an
6. Get a neat matrix inverse
7. Misc matrix and other functions

The documented code is in the jupyter notebook file NeatStateSpaceFunctions.ipynb which I extracted that code from the notebook and put it in a Python file called state_space_functions.py for people who want to import it as a module.

The file MatrixFunctions.ipynb which is the same code as MatrixFunctions is the matrix helper function such as get_inverse() and others.

The tests.py attempts to test state_space_functions.py by making it solve state space model homogenous, forced, and output responses and checking the solution. It is incomplete but has few good tests.

The file StateSpaceModel.ipynb has more functions and examples but it is an undocumented, unorganized version unlike NeatStateSpaceFunctions.ipynb I didn't remove it because it has examples which you can see to know how to use this code. You can see the example if you scroll down to the Example usage section in the StateSpaceModel.ipynbfile

Overall, this code helped me understand and solve Linear Systems problems so I wanted to share it, by no means is this a complete package or library.