Balanced truncation for linear switched systems

We propose a model order reduction approach for balanced truncation of linear switched systems. Such systems switch among a finite number of linear subsystems or modes. We compute pairs of controllability and observability Gramians corresponding to each active discrete mode by solving systems of cou...

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Bibliographic Details
Published in:Advances in computational mathematics 2018-12, Vol.44 (6), p.1845-1886
Main Authors: Gosea, Ion Victor, Petreczky, Mihaly, Antoulas, Athanasios C., Fiter, Christophe
Format: Article
Language:English
Subjects:
Automatic Control Engineering
Computational mathematics
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Computer Science
Controllability
Gramians
Linear systems
Mathematical and Computational Biology
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Model reduction
Observability (systems)
Reduced order models
Stability
Visualization
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Summary:We propose a model order reduction approach for balanced truncation of linear switched systems. Such systems switch among a finite number of linear subsystems or modes. We compute pairs of controllability and observability Gramians corresponding to each active discrete mode by solving systems of coupled Lyapunov equations. Depending on the type, each such Gramian corresponds to the energy associated to all possible switching scenarios that start or, respectively end, in a particular operational mode. In order to guarantee that hard to control and hard to observe states are simultaneously eliminated, we construct a transformed system, whose Gramians are equal and diagonal. Then, by truncation, directly construct reduced order models. One can show that these models preserve some properties of the original model, such as stability and that it is possible to obtain error bounds relating the observed output, the control input and the entries of the diagonal Gramians.
ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-018-9610-z