Paper Info
Title
Upper/lower bounds of generalized H2 norms in sampled-data systems with convergence rate analysis and discretization viewpoint.
Abstract
This paper considers linear time-invariant (LTI) sampled-data systems and studies their generalized H2 norms. They are defined as the induced norms from L2 to L∞, in which two types of the L∞ norm of the output are considered as the temporal supremum magnitude under the spatial ∞-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 H2 norms with operator-theoretic gridding approximation. This method leads to readily computable upper bounds as well as lower bounds of the generalized H2 norms, whose gaps tend to 0 at the rate of 1∕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.
Year
DOI
Venue
2017
10.1016/j.sysconle.2017.06.008
Systems & Control Letters
Keywords
Field
DocType
Sampled-data systems, L∞∕L2-induced norm,Discretization,Gridding,Operator-theoretic approach
Magnitude (mathematics),Discretization,Mathematical optimization,Control theory,Norm (social),Infimum and supremum,Sampled data systems,Rate of convergence,Mathematics,Computation
Journal
Volume
ISSN
Citations 
107
0167-6911
2
PageRank 
References 
Authors
0.39
4
2
Name
Order
Citations
PageRank
Jung Hoon Kim110420.47
Tomomichi Hagiwara228653.12