Upper/lower bounds of generalized H-2 norms in sampled-data systems with convergence rate analysis and discretization viewpoint
- Upper/lower bounds of generalized H-2 norms in sampled-data systems with convergence rate analysis and discretization viewpoint
- 김정훈; Tomomichi Hagiwara
- hybrid systems; sampled-data systems; disturbance rejection; H2 norm; Discretization; Gridding; Operator-theoretic approach
- Issue Date
- Systems & control letters
- VOL 107, NO 1-35
- 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.
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