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In this paper, we investigate the problem of robust L1 model reduction for linear parameter-varying (LPV) systems with parameter-varying delays. It is essential that the design of reduced-order system guarantees LPV error system to be asymptotically stable and satisfy peak-to-peak performance constraint with respect to all bounded peak value input signals. By using parameter-dependent Lyapunov function (PDLF), the sufficient conditions for the existence of the peak-to-peak criterion are established for error system with time delays for the first time, which realize the decoupling between the system matrices and PDLF matrices by introducing a slack matrix and applying Projection lemma. Under the conditions, the reducedorder system can be obtained in terms of linear matrix inequality (LMI) technology. Based on the approximate basis function and the gridding technique, the design problem of reduced-order system is cast into convex optimization problem subject to parameter LMI constraints. Finally, the validity of the proposed design method is illustrated by a numerical example. Keywordsrobust L1 model reduction; linear parameter-varying (LPV) systems; parameter-dependent Lyapunov function (PDLF)

Robust L1 Model Reduction for Linear Parameter-Varying Systems with Parameter-Varying Delays