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

In this paper, we investigate the problem of robust L-1 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 reduced-order 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.