Balanced truncation for linear switched systems
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.
Domains
Automatic Control Engineering
Origin : Files produced by the author(s)
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