| EPSRC Reference: |
GR/T20014/01 |
| Title: |
Analysis and Geometry in the Symmetrised Polydisc 2 |
| Principal Investigator: |
Young, Professor N |
| Other Investigators: |
|
| Researcher Co-Investigators: |
|
| Project Partners: |
|
| Department: |
Mathematics and Statistics |
| Organisation: |
Newcastle University |
| Scheme: |
Mathematics Small Grant PreFEC |
| Starts: |
01 July 2004 |
Ends: |
30 September 2005 |
Value (£): |
9,524
|
| EPSRC Research Topic Classifications: |
|
| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
|
|
| Related Grants: |
|
| Panel History: |
|
|
Summary on Grant Application Form |
|
The aim of the project is to elaborate new methods of constructing functions defined on a disc and meeting a complex set of specifications. The nature of these specifications is determined by the intended application: the design of automatic controllers of engineering systems. Accordingly, the functions to be constructed must be analytic, matrix-valued, take prescribed values at certain points and satisfy constraints on eigenvalues. In some cases of engineering interest the existence or otherwise of the desired function can be determined with the aim of classical function theory, but some recent developments in control theory lead to harder variants of the classical problems. In particular, the H-infinity approach to the problem of designing a stabilising controller for an imperfectly known unstable plant leads to a mathematical problem, known as the mu-synthesis problem, which is still unsolved. The PI and his collaborator have developed a new approach to some special cases of the mu-synthesis problem exploiting the theory of operators on Hilbert space.They have solved some of these cases and have revealed connections with deep problems in complex geometry, thereby solving a long-standing open question in several complex variables. In this project they will develop their methods further to envelop a wider class of control theoretic problems and a wider range of questions in complex geometry.
|
|
Key Findings |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
|
Potential use in non-academic contexts |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
|
Impacts |
|
| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
|
| Date Materialised |
|
|
|
|
Sectors submitted by the Researcher |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
| Project URL: |
|
| Further Information: |
|
| Organisation Website: |
http://www.ncl.ac.uk |