Semidefinite programming duality and linear time-invariant systems
نویسندگان
چکیده
منابع مشابه
Semidefinite programming duality and linear time-invariant systems
Several important problems in control theory can be reformulated as semidefinite programming problems, i.e., minimization of a linear objective subject to Linear Matrix Inequality (LMI) constraints. From convex optimization duality theory, conditions for infeasibility of the LMIs as well as dual optimization problems can be formulated. These can in turn be reinterpreted in control or system the...
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Several important problems in control theory can be reformulated as semide£nite programming problems, i.e., minimization of a linear objective subject to Linear Matrix Inequality (LMI) constraints. From convex optimization duality theory, conditions for infeasibility of the LMIs as well as dual optimization problems can be formulated. These can in turn be reinterpreted in control or system theo...
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It is well known that the duality theory for linear programming (LP) is powerful and elegant and lies behind algorithms such as simplex and interior-point methods. However, the standard Lagrangian for nonlinear programs requires constraint qualifications to avoid duality gaps. Semidefinite linear programming (SDP) is a generalization of LP where the nonnegativity constraints are replaced by a s...
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control scheme, in which different time scales for the rigid body subsystem dynamics and for the flexible dynamics are used (Canudas de Wit et al., 1996). An application of the two-time scale method is shown, for example, in Kang, Yeung, and Mills (2002). In summary, the aim of the authors to provide an upperlevel undergraduate and graduate textbook and a reference for experienced professionals...
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In a recent paper [8], Chan and Sun reported for semidefinite programming (SDP) that the primal/dual constraint nondegeneracy is equivalent to the dual/primal strong second order sufficient condition (SSOSC). This result is responsible for a number of important results in stability analysis of SDP. In this paper, we study duality of this type in nonlinear semidefinite programming (NSDP). We int...
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ژورنال
عنوان ژورنال: IEEE Transactions on Automatic Control
سال: 2003
ISSN: 0018-9286
DOI: 10.1109/tac.2002.806652