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Balanced truncation for linear switched systems

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Gosea,  Ion Victor
Max Planck Fellow Group for Data-Driven System Reduction and Identification, Max Planck Institute for Dynamics of Complex Technical Systems, Max Planck Society;

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Antoulas,  Athanasios C.
Max Planck Fellow Group for Data-Driven System Reduction and Identification, Max Planck Institute for Dynamics of Complex Technical Systems, Max Planck Society;

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Citation

Gosea, I. V., Petreczky, M., Antoulas, A. C., & Fiter, C. (2018). Balanced truncation for linear switched systems. Advances in Computational Mathematics, 44(6), 1845-1886. doi:10.1007/s10444-018-9610-z.


Cite as: http://hdl.handle.net/21.11116/0000-0000-2C09-6
Abstract
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.