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H model reduction for singular systems: continuous-time case

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4 Author(s)
Xu, S. ; Dept. of Mech. Eng., Univ. of Hong Kong, China ; Lam, J. ; Liu, W. ; Zhang, Q.

The problem of H model reduction for linear singular systems in the continuous-time case is considered. The objective is to find a reduced-order system such that the associated error system is admissible and satisfies a prescribed H norm bound constraint. Necessary and sufficient conditions for the solvability of this problem are obtained in terms of linear matrix inequalities (LMIs) and a coupling non-convex rank constraint set. An explicit parametrisation of all reduced-order systems is presented for the case when the related LMIs are feasible. A simple LMI condition without rank constraint is derived for the zeroth-order H approximation problem. All these results are obtained without decomposing the original system, which makes the design procedure simple and direct.

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Control Theory and Applications, IEE Proceedings -  (Volume:150 ,  Issue: 6 )