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In part (I) of this paper an optimization model of indefinite stochastic linear-quadratic (LQ) problem over an infinite time horizon with jumps is proposed and studied. In this sequel, the LQ control problem is further studied and solved completely. To be precise, we obtain a stabilizing optimal feedback control or determine that the LQ problem has no optimal solution by establishing several implication...
This paper studies a stochastic linear-quadratic (LQ) control problem over an infinite time horizon with Markovian jumps in parameter values, allowing the weighting matrices in the cost to be indefinite. Coupled generalized algebraic Riccati equations (CGAREs) involving pseudo inverse of a matrix are introduced. It is shown that the solvability of the LQ problem boils down to that of the CGAREs. However,...
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