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Free keywords:
Mathematics, Numerical Analysis, math.NA,cs.SY,
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.
