### 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 |

Publication status | Published - Jun 15 2000 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Control and Systems Engineering
- Electrical and Electronic Engineering

### Cite this

^{∞}problem for general plants in H

^{∞}and rational weights.

*Systems and Control Letters*,

*40*(2), 83-95.

**A Hamiltonian-based solution to the two-block H ^{∞} problem for general plants in H^{∞} and rational weights.** / Hirata, Kentaro; Yamamoto, Yutaka; Tannenbaum, Allen R.

Research output: Contribution to journal › Article

^{∞}problem for general plants in H

^{∞}and rational weights',

*Systems and Control Letters*, vol. 40, no. 2, pp. 83-95.

^{∞}problem for general plants in H

^{∞}and rational weights. Systems and Control Letters. 2000 Jun 15;40(2):83-95.

}

TY - JOUR

T1 - A Hamiltonian-based solution to the two-block H∞ problem for general plants in H∞ and rational weights

AU - Hirata, Kentaro

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

UR - http://www.scopus.com/inward/record.url?scp=0347997536&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0347997536&partnerID=8YFLogxK

M3 - Article

VL - 40

SP - 83

EP - 95

JO - Systems and Control Letters

JF - Systems and Control Letters

SN - 0167-6911

IS - 2

ER -