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Stabilization of Linear Systems with Structured Perturbations

Lu, Wei-Min and Zhou, Kemin and Doyle, John C. (1993) Stabilization of Linear Systems with Structured Perturbations. California Institute of Technology , Pasadena, CA. (Unpublished)

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The problem of stabilization of linear systems with bounded structured uncertainties are considered in this paper. Two notions of stability, denoted quadratic stability (Q-stability) and μ-stability, are considered, and corresponding notions of stabilizability and detectability are defined. In both cases, the output feedback stabilization problem is reduced via a separation argument to two simpler problems: full information (FI) and full control (FC). The set of all stabilizing controllers can be parametrized as a linear fractional transformation (LFT) on a free stable parameter. For Q-stability, stabilizability and detectability can in turn be characterized by Linear Matrix Inequalities (LMIs), and the FI and FC Q-stabilization problems can be solved using the corresponding LMIs. In the standard one-dimensional case the results in this paper reduce to well-known results on controller parametrization using state-space methods, although the development here relies more heavily on elegant LFT machinery and avoids the need for coprime factorizations.

Item Type:Report or Paper (Technical Report)
Doyle, John C.0000-0002-1828-2486
Additional Information:The authors would like to thank Prof. A. Packard at UC Berkeley for helpful discussion. They also gratefully acknowledge helpful comments about the previous versions of this paper from C. Beck, B. Bodenheimer, J. Morris, F. Paganini and J. Tierno. Support for this work was provided by NSF, AFOSR, and ONR.
Group:Control and Dynamical Systems Technical Reports
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)UNSPECIFIED
Office of Naval Research (ONR)UNSPECIFIED
Record Number:CaltechCDSTR:1993.014
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ID Code:28058
Deposited By: Imported from CaltechCDSTR
Deposited On:01 Sep 2006
Last Modified:27 Feb 2020 17:57

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