State Space

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In a lot of my work I use state space matrices for control systems design.

 

This is my go-to way of visualising the dimensions of matrices in a linear time invariant state space system

given by the following equations:

x = Ax+Bu

y = Cx+Du

Understanding this really helps when you're to hand-coding portions of controller-plant systems for analyses such as stability, controllability and robustness and have to do a lot of state substitutions and forget what sizes your matrices need to be to correctly multiply together!

The distribution of colour is a heat-map of sorts based on the sizes of state space systems I worked with during university projects while I was studying for qualifications in aerospace systems engineering.

As you can see, I worked with a lot of quite small SISO or few input-output systems and only a few very large MIMO systems.

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