0
votes
1answer
55 views

How does the z transform work in practice?

What I've found I've implemented a PID controller using the equations 7 and 9 of this article, which states that: $$\frac{U(s)}{E(s)}=K_p+\frac{K_i}{s}+K_ds$$ Translates to ...
0
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1answer
89 views

Linear time varying into linear time invariant.

My original problem, is to transform Linear time varying systems of the form , for example: $$\begin{bmatrix}\dot{x1} \\ \dot{x2} \end{bmatrix} = \begin{bmatrix} -3t^2 & 0 \\ 6t^5 & -6t^2 ...
1
vote
2answers
645 views

Decomposition of a unitary matrix via Householder matrices

If $U$ is unitary, how can I show that there exist $w_{1},w_{2},...,w_{k}\in \mathbb{C}^{n}$, $k\leq n$, and $\theta_{1},\theta_{2},...,\theta_{n}\in \mathbb{R}$ such that $U=U_{w_{1}}U_{w_{2}}\cdots ...