Model reduction by moment matching at discontinuous signals via hybrid output regulation

The problem of model reduction by moment matching for LTI systems driven by specific exogenous signals is tackled here in the case of discontinuous input signals. In particular, we consider a class of piecewise-continuous signals that can be generated as the output of suitably defined linear hybrid systems in the presence of periodic jumps. The proposed class of reduced-order models, which are given in terms of linear time-varying hybrid systems, is constructed by borrowing techniques from the theory of output regulation for linear hybrid systems. The resulting approach combines rather mild constructive assumptions, requiring only a generically satisfied non-resonance condition, with a significant reduction of the state dimension. In fact, a reduced-order model with state dimension matching the number of outputs can be obtained regardless of the number of original states. Finally, the performance of the methodology is assessed by means of numerical simulations.