A Hamiltonian-based solution to the two-block H∞ problem for general plants in H∞ and rational weights

Kentaro Hirata; Yutaka Yamamoto; Allen R. Tannenbaum

doi:10.1016/S0167-6911(00)00005-0

A Hamiltonian-based solution to the two-block H^∞ problem for general plants in H^∞ and rational weights

Kentaro Hirata, Yutaka Yamamoto, Allen R. Tannenbaum

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

A complete skew-Toeplitz-type solution to the two-block H^∞ problem for infinite-dimensional stable plants with rational weights is derived with a basis-free proof. The solution consists of one Riccati equation with a rank criterion for a transcendental function of a certain Hamiltonian. This gives a natural extension of the well-known formula for the one-block case. An example is given to illustrate the result.

Original language	English
Pages (from-to)	83-95
Number of pages	13
Journal	Systems and Control Letters
Volume	40
Issue number	2
DOIs	https://doi.org/10.1016/S0167-6911(00)00005-0
Publication status	Published - Jun 15 2000
Externally published	Yes

Keywords

Distributed systems
H control
Optimal sensitivity
Skew-Toeplitz theory
Two-block problem

ASJC Scopus subject areas

Control and Systems Engineering
Computer Science(all)
Mechanical Engineering
Electrical and Electronic Engineering

Access to Document

10.1016/S0167-6911(00)00005-0

Cite this

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abstract = "A complete skew-Toeplitz-type solution to the two-block H∞ problem for infinite-dimensional stable plants with rational weights is derived with a basis-free proof. The solution consists of one Riccati equation with a rank criterion for a transcendental function of a certain Hamiltonian. This gives a natural extension of the well-known formula for the one-block case. An example is given to illustrate the result.",

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AU - Yamamoto, Yutaka

AU - Tannenbaum, Allen R.

PY - 2000/6/15

Y1 - 2000/6/15

N2 - A complete skew-Toeplitz-type solution to the two-block H∞ problem for infinite-dimensional stable plants with rational weights is derived with a basis-free proof. The solution consists of one Riccati equation with a rank criterion for a transcendental function of a certain Hamiltonian. This gives a natural extension of the well-known formula for the one-block case. An example is given to illustrate the result.

AB - A complete skew-Toeplitz-type solution to the two-block H∞ problem for infinite-dimensional stable plants with rational weights is derived with a basis-free proof. The solution consists of one Riccati equation with a rank criterion for a transcendental function of a certain Hamiltonian. This gives a natural extension of the well-known formula for the one-block case. An example is given to illustrate the result.

KW - Distributed systems

KW - H control

KW - Optimal sensitivity

KW - Skew-Toeplitz theory

KW - Two-block problem

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