Balanced truncation model reduction for linear time-varying systems

N. Lang, J. Saak and T. Stykel

Mathematical and Computer Modelling of Dynamical Systems, 2016, vol. 22, issue 4, 267-281

Abstract: A practical procedure based on implicit time integration methods applied to the differential Lyapunov equations arising in the square root balanced truncation method is presented. The application of high-order time integrators results in indefinite right-hand sides of the algebraic Lyapunov equations that have to be solved within every time step. Therefore, classical methods exploiting the inherent low-rank structure often observed for practical applications end up in complex data and arithmetic. Avoiding the additional effort in treating complex quantities, a symmetric indefinite factorization of both the right-hand side and the solution of the differential Lyapunov equations is applied.

Date: 2016
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DOI: 10.1080/13873954.2016.1198386

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