SIMPLIFYING THE H-INFINITY THEORY VIA LOOP-SHIFTING, MATRIX-PENCIL AND DESCRIPTOR CONCEPTS
The 2-Riccati H∞ controller formulas and derivations are simplified via various 'loop-shifting' transformations that are naturally expressed in terms of a degree-one polynomial system matrix (PSM) closely related to the Luenberger descriptor form of a system. The technique enables one with...
| Main Authors: | , , |
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| Format: | Journal article |
| Jezik: | English |
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1989
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| _version_ | 1826275247338291200 |
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| author | Safonov, M Limebeer, D Chiang, R |
| author_facet | Safonov, M Limebeer, D Chiang, R |
| author_sort | Safonov, M |
| collection | OXFORD |
| description | The 2-Riccati H∞ controller formulas and derivations are simplified via various 'loop-shifting' transformations that are naturally expressed in terms of a degree-one polynomial system matrix (PSM) closely related to the Luenberger descriptor form of a system. The technique enables one without loss of generality to restrict attention to the simple case in which D11 = 0, D22 = 0, D12T = [0 I], D21 = [0 I], D12TC1 = 0 and B1D21T = 0. Matrix-fraction descriptions (MFDs) for the algebraic Riccati equation solutions afford another change of variables, which brings the 2-Riccati H∞ controller formulas into a cleaner, more symmetric descriptor form having the important practical advantage that it eliminates the numerical difficulties that can occur in cases where one or both of the Riccati solutions, P and Q, blow up and in cases where I - QP is nearly singular. Numerical difficulties previously associated with verifying the existence conditions P≥0, Q≥0, and λmax (QP) <1 are largely eliminated by equivalent alternative conditions. |
| first_indexed | 2024-03-06T22:55:48Z |
| format | Journal article |
| id | oxford-uuid:6053333b-94a5-4e29-b51b-5643a171d63c |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T22:55:48Z |
| publishDate | 1989 |
| record_format | dspace |
| spelling | oxford-uuid:6053333b-94a5-4e29-b51b-5643a171d63c2022-03-26T17:52:47ZSIMPLIFYING THE H-INFINITY THEORY VIA LOOP-SHIFTING, MATRIX-PENCIL AND DESCRIPTOR CONCEPTSJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:6053333b-94a5-4e29-b51b-5643a171d63cEnglishSymplectic Elements at Oxford1989Safonov, MLimebeer, DChiang, RThe 2-Riccati H∞ controller formulas and derivations are simplified via various 'loop-shifting' transformations that are naturally expressed in terms of a degree-one polynomial system matrix (PSM) closely related to the Luenberger descriptor form of a system. The technique enables one without loss of generality to restrict attention to the simple case in which D11 = 0, D22 = 0, D12T = [0 I], D21 = [0 I], D12TC1 = 0 and B1D21T = 0. Matrix-fraction descriptions (MFDs) for the algebraic Riccati equation solutions afford another change of variables, which brings the 2-Riccati H∞ controller formulas into a cleaner, more symmetric descriptor form having the important practical advantage that it eliminates the numerical difficulties that can occur in cases where one or both of the Riccati solutions, P and Q, blow up and in cases where I - QP is nearly singular. Numerical difficulties previously associated with verifying the existence conditions P≥0, Q≥0, and λmax (QP) <1 are largely eliminated by equivalent alternative conditions. |
| spellingShingle | Safonov, M Limebeer, D Chiang, R SIMPLIFYING THE H-INFINITY THEORY VIA LOOP-SHIFTING, MATRIX-PENCIL AND DESCRIPTOR CONCEPTS |
| title | SIMPLIFYING THE H-INFINITY THEORY VIA LOOP-SHIFTING, MATRIX-PENCIL AND DESCRIPTOR CONCEPTS |
| title_full | SIMPLIFYING THE H-INFINITY THEORY VIA LOOP-SHIFTING, MATRIX-PENCIL AND DESCRIPTOR CONCEPTS |
| title_fullStr | SIMPLIFYING THE H-INFINITY THEORY VIA LOOP-SHIFTING, MATRIX-PENCIL AND DESCRIPTOR CONCEPTS |
| title_full_unstemmed | SIMPLIFYING THE H-INFINITY THEORY VIA LOOP-SHIFTING, MATRIX-PENCIL AND DESCRIPTOR CONCEPTS |
| title_short | SIMPLIFYING THE H-INFINITY THEORY VIA LOOP-SHIFTING, MATRIX-PENCIL AND DESCRIPTOR CONCEPTS |
| title_sort | simplifying the h infinity theory via loop shifting matrix pencil and descriptor concepts |
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