Observability of Uncertain Nonlinear Systems Using Interval Analysis
Abstract
:1. Introduction
2. Materials and Methods
2.1. Interval Arithmetics
2.2. Observability of Uncertain Nonlinear Systems
2.3. Algorithm for Studying the Observability of Nonlinear Systems
Algorithm1Robust observability 
 INPUT: $f\left(\right)open="("\; close=")">x,\alpha $, $h\left(\right)open="("\; close=")">x,\beta $, ${D}_{x}$ and ${\delta}^{I}=\left(\right)open="\{"\; close="\}">{\alpha}^{I},{\beta}^{I}$ 

2.3.1. Initialization of the Algorithm
2.3.2. Calculation of Lie Derivatives for Proving Distinguishability Using the Power Series
2.3.3. Example: Direct Calculation of Lie Derivatives
2.3.4. Applying the Local Condition
2.3.5. Final Remarks
3. Results of the Algorithm
3.1. Example 1
3.2. Example 2
3.3. Example 3
3.4. Remark to the Presented Examples
4. Discussion
Author Contributions
Funding
Conflicts of Interest
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Paradowski, T.; Lerch, S.; Damaszek, M.; Dehnert, R.; Tibken, B. Observability of Uncertain Nonlinear Systems Using Interval Analysis. Algorithms 2020, 13, 66. https://doi.org/10.3390/a13030066
Paradowski T, Lerch S, Damaszek M, Dehnert R, Tibken B. Observability of Uncertain Nonlinear Systems Using Interval Analysis. Algorithms. 2020; 13(3):66. https://doi.org/10.3390/a13030066
Chicago/Turabian StyleParadowski, Thomas, Sabine Lerch, Michelle Damaszek, Robert Dehnert, and Bernd Tibken. 2020. "Observability of Uncertain Nonlinear Systems Using Interval Analysis" Algorithms 13, no. 3: 66. https://doi.org/10.3390/a13030066