State-space Control

Resources

https://people.isy.liu.se/en/rt/claal20/TSRT09/rteoh3_en.pdf

State-space control relies heavily on Matrices.

Model Form

$\dot{\vec{x}}=A\cdot \vec{x}+B\cdot \vec{u}$ $\vec{z}=C\cdot \vec{x}+D\cdot \vec{u}$

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Reachability

Answers the question: can we move the system to any point in the state space in finite time?

Controllability

Answers the question: can we stabilise the system around the origin of the state space in finite time?

Stabilisability

Answers the question: can the system be stabilised when closing the loop with a suitably designed $u=Kx$?

Observability

Answers the question: can we observe the system states without an up-to-date version of $\vec{x}$?