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Article

Transformation of Uncertain Linear Systems with Real Eigenvalues into Cooperative Form: The Case of Constant and Time-Varying Bounded Parameters

1
ENSTA Bretagne, Lab-STICC, 29806 Brest, France
2
Chair of Mechatronics, University of Rostock, D-18059 Rostock, Germany
*
Author to whom correspondence should be addressed.
Academic Editor: Günther Raidl
Algorithms 2021, 14(3), 85; https://doi.org/10.3390/a14030085
Received: 18 January 2021 / Revised: 2 March 2021 / Accepted: 3 March 2021 / Published: 8 March 2021
(This article belongs to the Special Issue Algorithms for Reliable Estimation, Identification and Control II)
Continuous-time linear systems with uncertain parameters are widely used for modeling real-life processes. The uncertain parameters, contained in the system and input matrices, can be constant or time-varying. In the latter case, they may represent state dependencies of these matrices. Assuming bounded uncertainties, interval methods become applicable for a verified reachability analysis, for feasibility analysis of feedback controllers, or for the design of robust set-valued state estimators. The evaluation of these system models becomes computationally efficient after a transformation into a cooperative state-space representation, where the dynamics satisfy certain monotonicity properties with respect to the initial conditions. To obtain such representations, similarity transformations are required which are not trivial to find for sufficiently wide a-priori bounds of the uncertain parameters. This paper deals with the derivation and algorithmic comparison of two different transformation techniques for which their applicability to processes with constant and time-varying parameters has to be distinguished. An interval-based reachability analysis of the states of a simple electric step-down converter concludes this paper. View Full-Text
Keywords: interval analysis; cooperative system models; reachability analysis; wrapping effect interval analysis; cooperative system models; reachability analysis; wrapping effect
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MDPI and ACS Style

Rauh, A.; Kersten, J. Transformation of Uncertain Linear Systems with Real Eigenvalues into Cooperative Form: The Case of Constant and Time-Varying Bounded Parameters. Algorithms 2021, 14, 85. https://doi.org/10.3390/a14030085

AMA Style

Rauh A, Kersten J. Transformation of Uncertain Linear Systems with Real Eigenvalues into Cooperative Form: The Case of Constant and Time-Varying Bounded Parameters. Algorithms. 2021; 14(3):85. https://doi.org/10.3390/a14030085

Chicago/Turabian Style

Rauh, Andreas, and Julia Kersten. 2021. "Transformation of Uncertain Linear Systems with Real Eigenvalues into Cooperative Form: The Case of Constant and Time-Varying Bounded Parameters" Algorithms 14, no. 3: 85. https://doi.org/10.3390/a14030085

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