# Coprime Factor Reduction of Parameter Varying Controller

• Saragih, Roberd (Industrial and Financial Mathematics Group, Faculty of Mathematics and Natural Science, Institut Teknologi Bandung) ;
• Widowati, Widowati (Department of Mathematics, Diponegoro University)
• Published : 2008.12.31

#### Abstract

This paper presents an approach to order reduction of linear parameter varying controller for polytopic model. Feasible solutions which satisfy relevant linear matrix inequalities for constructing full-order parameter varying controller evaluated at each polytopic vertices are first found. Next, sufficient conditions are derived for the existence of a right coprime factorization of parameter varying controller. Furthermore, a singular perturbation approximation for time invariant systems is generalized to reduce full-order parameter varying controller via parameter varying right coprime factorization. This generalization is based on solutions of the parameter varying Lyapunov inequalities. The closed loop performance caused by using the reduced order controller is developed. To examine the performance of the reduced-order parameter varying controller, the proposed method is applied to reduce vibration of flexible structures having the transverse-torsional coupled vibration modes.

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