A new representation of lifted systems with applications

Lifting, i.e. discretization with built-in intersample behavior, is an emerging technique for the analysis and design sampled-data systems. The applicability of the lifting technique, however, is considerably limited due to difficulties in dealing with parameters of the lifted systems, which are operators over infinite-dimensional spaces rather than finite-dimensional matrices. The purpose of this paper is to introduce a new representation for the parame-ters of the lifted systems. This representation simplifies considerably algebraic manipulation over those parameters. It is based on expressing infinite-dimensional operators by dynamical systems with two-point boundary conditions operating on a finite time interval. A technical machinery, which enables one to reduce algebraic manipulation over the parameters of the lifted systems to simple matrix manipulations in the state-space, is developed in the paper on the basis of the new representation. It is believed that the new representation together with the developed machinery extends considerably the scope of applicability and enhances the efficiency of the lifting technique. Several applications considered in the paper (compu-tational issues in sampled-data H2 and H ∞ control and Riccati equations for lifted systems) demonstrate the benefits of the proposed representation and its capabilities