### 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 |
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Pages (from-to) | 83-95 |

Number of pages | 13 |

Journal | Systems and Control Letters |

Volume | 40 |

Issue number | 2 |

DOIs | |

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

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## Cite this

Hirata, K., Yamamoto, Y., & Tannenbaum, A. R. (2000). A Hamiltonian-based solution to the two-block H

^{∞}problem for general plants in H^{∞}and rational weights.*Systems and Control Letters*,*40*(2), 83-95. https://doi.org/10.1016/S0167-6911(00)00005-0