Robust peak-to-peak model reduction for uncertain linear systems: Continuous- and discrete-time cases

This paper investigates the problem of robust peak-to-peak model reduction for continuous- and discrete-time uncertain linear systems. For a given stable system, our purpose is to construct reduced-order systems, such that the error system between these two models is asymptotically stable and has a guaranteed peak-to-peak performance. This problem is solved by using the projection lemma and sufficient conditions are obtained for the existence of admissible reduced-order models in terms of linear matrix inequalities (LMIs) plus matrix inverse constraints. Since these obtained conditions are not expressed as strict LMIs, the cone complementarity linearization (CCL) method is exploited to cast them into nonlinear minimization problems subject to LMI constraints, which can be readily solved by standard numerical software. In addition, the development of zerothorder model is also presented. Both continuous- and discrete-time cases are considered. The efficiency of the proposed methods is demonstrated via numerical examples.