Tartalomjegyzék

Standard 1D order reduction

TELJES MATLAB SCRIPT KIEGÉSZÍTŐ FÜGGVÉNYEKKEL

file:   standard_1d_order_reduction.m
author: Peter Polcz <ppolcz@gmail.com>

Created on 2017. September 02.

Output:

┌standard_1d_order_reduction
│   - Persistence for `standard_1d_order_reduction` reused (inherited) [run ID: 9151, 2017.09.02. Saturday, 11:38:12]
│   - Script `standard_1d_order_reduction` backuped

Some preliminary important linear algebra facts

Image and kernel space of linear transformation $y = Ax$

Let us detonte $\mathcal U = \rm{Im}(A)$, $\mathcal V = \rm{Ker}(A)$, where $A \in \mathbb R^{n \times n}$. It is not necessary that $\mathcal U = \mathcal V^\perp$.

A = [
    0 1
    0 0
    ];

U = orth(A)
V = null(A)

rank([U V])

Output:

U =
     1
     0
V =
    -1
     0
ans =
     1

Controllability and observability

$$ \begin{aligned} &\dot x = A x + B y \\ &y = C x \end{aligned} $$

The state space could be partitioned as follows:

$$ X = X_{co} \otimes X_{c \bar o} \otimes X_{\bar c o} \otimes X_{\bar c \bar o} $$

$X_{\cdot \cdot}$ are pairwise orthogonal subsets of the state space.

End of the script.

Output:

└ 0.03252 [sec]

Published with MATLAB® R2015a, and sanitarized by BeautifulSoup (Python script using BSoup is written by Polcz).