m (→Affine Parametric Second-Order System: actually make indices uniform) |
m (→Affine Parametric Linear Time-Invariant System: make indices uniform; add + after A_0) |
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Line 83: | Line 83: | ||
:<math> |
:<math> |
||
\begin{align} |
\begin{align} |
||
− | (E_0 + \sum_{ |
+ | (E_0 + \sum_{j=1}^{P_E} p^E_j E_j)\dot{x}(t) &= (A_0 + \sum_{i=1}^{P_A} p^A_i A_i) x(t) + Bu(t),\\ |
y(t) &= Cx(t), |
y(t) &= Cx(t), |
||
\end{align} |
\end{align} |
||
Line 91: | Line 91: | ||
<math>E_0 \in \mathbb{R}^{N \times N}</math>, |
<math>E_0 \in \mathbb{R}^{N \times N}</math>, |
||
− | <math> |
+ | <math>E_j \in \mathbb{R}^{N \times N}</math>, |
<math>A_0 \in \mathbb{R}^{N \times N}</math>, |
<math>A_0 \in \mathbb{R}^{N \times N}</math>, |
||
− | <math> |
+ | <math>A_i \in \mathbb{R}^{N \times N}</math>, |
<math>B \in \mathbb{R}^{N \times M}</math>, |
<math>B \in \mathbb{R}^{N \times M}</math>, |
||
<math>C \in \mathbb{R}^{Q \times N}</math>. |
<math>C \in \mathbb{R}^{Q \times N}</math>. |
||
− | |||
===Second-Order System=== |
===Second-Order System=== |
Revision as of 10:58, 9 August 2022
Note: This page has not been verified by our editors.
Benchmark Model Overview
This page outlines the types of models that are used as benchmark systems.
For this general summary we assume an input ,
a state
and an output
.
Linear Time-Invariant System
with:
,
,
,
.
Linear Time-Varying System
with:
,
,
,
.
Quadratic-Bilinear System
with:
,
,
,
,
,
.
Nonlinear Time-Invariant System
with:
,
,
,
,
.
Affine Parametric Linear Time-Invariant System
with:
,
,
,
,
,
.
Second-Order System
with:
,
,
,
,
.
Nonlinear Second-Order System
with:
,
,
,
,
,
.
Affine Parametric Second-Order System
with:
,
,
,
,
,
,
,
.