Balanced Truncation Model Order Reduction for LTI Systems with many Inputs or Outputs

We discuss balanced truncation (BT) based meth- ods for model order reduction (MOR) of linear time invariant (LTI) systems with many input or many output terminals. Applying BT methods makes it necessary to balance the system, which is equivalent to finding the controllability and observability Gramian of the system in a special diagonal form. The Cholesky factors of these Gramians are efficiently computable as solutions of dual Lyapunov equations for systems with only few inputs and outputs. After a brief introduction and a short recollection of basic knowledge of BT, we show a method to get the Gramians' factors also for systems with many inputs and outputs with the help of the Gauss-Kronrod quadrature formula. We show some numerical results using this quadrature rule and explain how to get the BT reduced order model out of these results. I. INTRODUCTION

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