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## The unmixing problem (1991)

Venue: | IMA J. Math. Control & Information |

Citations: | 1 - 0 self |

### Citations

40 | Theory of Matrices, volume 1 - Gantmacher - 1959 |

22 |
Global adaptive stabilization in the absence of information on the sign of the high frequency gain,” in Analysis and
- Willems, Byrnes
- 1984
(Show Context)
Citation Context ...e. Finding the premultiplier which best diagonalizes the plant could be performed automatically. Thus, such a procedure could possibly turn out to be feasible for industrial multivariable control. In =-=[10]-=-, Willems and Byrnes solved a problem of adaptive stabilization for a class of single-input single-output systems with unknown sign of the gain. Trying to generalize this result to the multivariable c... |

20 |
Adaptive stabilization of multivariable linear systems,
- Byrnes, Willems
- 1984
(Show Context)
Citation Context ... adaptive stabilization for a class of single-input single-output systems with unknown sign of the gain. Trying to generalize this result to the multivariable case, the unmixing problem was raised in =-=[3]-=-. Some open problems in [3] were settled by Martensson in [8]. A further development for the case m — 3 was presented by Zhu in [11]. Recently, the results in [8] were used by Ilchmann, Logemann, and ... |

11 |
Adaptive Stabilization.
- Martensson
- 1986
(Show Context)
Citation Context ... with a stable system H(s). Equivalently, the transfer function of the plant can be written as G(s) = (/ + ^GoH(s)) \GQ, where Go = lim,^co sG(s). Using the feedback u = — ky, it is easy to see (e.g. =-=[8]-=-) that for k large, asymptotically the poles of the closed-loop system will be the poles of H(s), by assumption stable, together with m poles (where m is the number of inputs and outputs) at the zeros... |

7 |
Introduction to Group Theory with Applications. Academic Press. at Penn State U niversity
- BURNS
- 1977
(Show Context)
Citation Context ... which this group fails to unmix. Zhu [11] has an interesting approach to the problem of unmixing 80(3): By using a homomorphism p from §11(2) to 80(3), known as the adjoint representation for SU(2) (=-=[2]-=-), it is shown that the a-unmixing problem for 80(3) "lifts" to the a/2-unmixing problem for SU(2). Precisely, if A is a/2-unmixing for 811(2), then p(A) is a-unmixing for 80(3). Furthermore, with ( !... |

5 |
An adaptive servomechanism for a class of infinite-dimensional systems
- LOGEMANN, ILCHMANN
- 1991
(Show Context)
Citation Context ...were settled by Martensson in [8]. A further development for the case m — 3 was presented by Zhu in [11]. Recently, the results in [8] were used by Ilchmann, Logemann, and Martensson in [7], [5], and =-=[6]-=-. The present paper is mainly based upon — and supersedes — [8, Section 6.2]. From this point on, we leave the background, and concentrate entirely on the mathematical problem. Consequently, we will w... |

4 |
Singular values of a matrix
- AMIR-MOEZ, HORN
- 1958
(Show Context)
Citation Context ...and O 6 0(n). Then the eigenvalues of OP are contained in the convex cone spanned by the eigenvalues ofO. In particular, if <r(O) € C+, then a{OP) eC+. The proof, which is elementary, can be found in =-=[1]-=-. A direct proof of the statement in the last sentence can be constructed by noting that the conclusion is equivalent to the asymptotic stability of the autonomous system z = —OPx. It is easy to show ... |

2 |
Adaptive stabilization of infinite dimensional systems
- LOGEMANN, MARTENSSON
- 1990
(Show Context)
Citation Context ...oblems in [3] were settled by Martensson in [8]. A further development for the case m — 3 was presented by Zhu in [11]. Recently, the results in [8] were used by Ilchmann, Logemann, and Martensson in =-=[7]-=-, [5], and [6]. The present paper is mainly based upon — and supersedes — [8, Section 6.2]. From this point on, we leave the background, and concentrate entirely on the mathematical problem. Consequen... |

1 |
High-gain stabilization of multivariable linear systems
- ILCHMANN, LOGEMANN
- 1991
(Show Context)
Citation Context ...s in [3] were settled by Martensson in [8]. A further development for the case m — 3 was presented by Zhu in [11]. Recently, the results in [8] were used by Ilchmann, Logemann, and Martensson in [7], =-=[5]-=-, and [6]. The present paper is mainly based upon — and supersedes — [8, Section 6.2]. From this point on, we leave the background, and concentrate entirely on the mathematical problem. Consequently, ... |

1 |
Special Functions and the Theory of Group Representations
- VlLENKIN
- 1968
(Show Context)
Citation Context ...ar measure, which we will denote by dg. With pi = Jn dg, clearly there can be no unmixing set with cardinality less than l//i. The measure dg can be explicitly expressed in terms of the Euler angles, =-=[9]-=-, n - 1 k k=ij=i where _ A r(*/2) A » ~ LL 2**12 • Note that, for n > 2, this formula also predicts that our method, which can be described as mapping a lattice on the Af-torus to SO(n) via the Euler ... |

1 |
A finite spectrum unmixing set for GL(3,K
- ZHU
- 1989
(Show Context)
Citation Context ...result to the multivariable case, the unmixing problem was raised in [3]. Some open problems in [3] were settled by Martensson in [8]. A further development for the case m — 3 was presented by Zhu in =-=[11]-=-. Recently, the results in [8] were used by Ilchmann, Logemann, and Martensson in [7], [5], and [6]. The present paper is mainly based upon — and supersedes — [8, Section 6.2]. From this point on, we ... |