A primal-dual semidefinite programming approach to linear quadratic control

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)1442-1447
Journal / PublicationIEEE Transactions on Automatic Control
Issue number9
Publication statusPublished - Sep 2001
Externally publishedYes


We study a deterministic linear-quadratic (LQ) control problem over an infinite horizon, without the restriction that the control cost matrix R or the state cost matrix Q be positive-definite. We develop a general approach to the problem based on semidefinite programming (SDP) and related duality analysis. We show that the complementary duality condition of the SDP is necessary and sufficient for the existence of an optimal LQ control under a certain stability condition (which is satisfied automatically when Q is positive-definite). When the complementary duality does hold, an optimal state feedback control is constructed explicitly in terms of the solution to the primal SDP.

Research Area(s)

  • Complementary duality, Generalized Riccati equation, LQ control, Semidefinite programming