Equivalence of robust stabilization and robust performance via feedback
| dc.creator | Ball, J. A. | |
| dc.creator | Fang, Q. | |
| dc.creator | Groenewald, G. J. | |
| dc.creator | ter Horst, S. | |
| dc.date | 2008-08-19 | |
| dc.date.accessioned | 2026-07-07T09:57:20Z | |
| dc.date.available | 2026-07-07T09:57:20Z | |
| dc.description | One approach to robust control for linear plants with structured uncertainty as well as for linear parameter-varying (LPV) plants (where the controller has on-line access to the varying plant parameters) is through linear-fractional-transformation (LFT) models. Control issues to be addressed by controller design in this formalism include robust stability and robust performance. Here robust performance is defined as the achievement of a uniform specified $L^{2}$-gain tolerance for a disturbance-to-error map combined with robust stability. By setting the disturbance and error channels equal to zero, it is clear that any criterion for robust performance also produces a criterion for robust stability. Counter-intuitively, as a consequence of the so-called Main Loop Theorem, application of a result on robust stability to a feedback configuration with an artificial full-block uncertainty operator added in feedback connection between the error and disturbance signals produces a result on robust performance. The main result here is that this performance-to-stabilization reduction principle must be handled with care for the case of dynamic feedback compensation: casual application of this principle leads to the solution of a physically uninteresting problem, where the controller is assumed to have access to the states in the artificially-added feedback loop. Application of the principle using a known more refined dynamic-control robust stability criterion, where the user is allowed to specify controller partial-state dimensions, leads to correct robust-performance results. These latter results involve rank conditions in addition to Linear Matrix Inequality (LMI) conditions. | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/0808.2578 | |
| dc.identifier | http://arxiv.org/abs/0808.2578 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/167307 | |
| dc.subject | Optimization and Control | |
| dc.subject | 93D15; 93B52, 93D09, 47A48, 47A63 | |
| dc.title | Equivalence of robust stabilization and robust performance via feedback | |
| dc.type | text |