Upper/lower bounds of generalized H2 norms in sampled-data systems with convergence rate analysis and discretization viewpoint

This paper considers linear time-invariant (LTI) sampled-data systems and studies their generalized H-2 norms. They are defined as the induced norms from L-2 to L-infinity, in which two types of the L-infinity norm of the output are considered as the temporal supremum magnitude under the spatial infinity-norm and 2-norm. The input/output relation of sampled-data systems is first formulated under their lifting-based treatment. We then develop a method for computing the generalized H-2 norms with operator-theoretic gridding approximation. This method leads to readily computable upper bounds as well as lower bounds of the generalized H-2 norms, whose gaps tend to 0 at the rate of 1/root N with the gridding approximation parameter N. An approximately equivalent discretization method of the generalized plant is further provided as a fundamental step to addressing the controller synthesis problem of minimizing the generalized H2 norms of sampled-data systems. Finally, a numerical example is given to show the effectiveness of the computation method. (C) 2017 Elsevier B.V. All rights reserved.