Linear matrix inequalities, Riccati equations, and indefinite stochastic linear quadratic controls

By Mustapha Ait Rami, Xun Yu Zhou. IEEE Transactions on Automatic Control, 2000

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Stochastic Linear Quadratic Optimal Control Problems in Infinite Horizon (2016, methodology): “Stochastic LQ problems in an infinite horizon and the associated algebraic Riccati equations (AREs, for short) were treated in [2,3] via the linear matrix inequality and semidefinite programming techniques.”
Optimal Consensus Seeking in a Network of Multiagent Systems: An LMI Approach (2010, background): “In [29]–[ 31 ], it is shown that the LQR problem can be formulated as a minimization problem that is constrained to a set of LMIs.”
Performance bounds for linear stochastic control (2009, background): “The gap can be large, of course, for two reasons: our suboptimal controller is substantially suboptimal, or, our lower bound is poor (for this problem instance).”
Well-posedness and attainability of indefinite stochastic linear quadratic control in infinite time horizon (2000, background): “Subsequent researches include extensions to the cases of discrete-time [12], multi-objective [11], and inÿnite time horizon [1].”