Abstract
In this paper, we investigate the near-optimal control for a singularly perturbed linear stochastic singular system with Markovian jumping parameters. Firstly, we warrant the given system has an impulse-free solution. Secondly, by means of the singular value decomposition, the existence of solution are obtained for the singularly perturbed stochastic generalized coupled differential Riccati equation and establish an existence of solution to parameter-independent system for the stochastic generalized coupled differential Riccati equation. As an application, we apply the existence results to consider the near-optimal control of singularly perturbed linear stochastic singular system with Markovian jumping parameters, and obtain the desired explicit representation of the optimal controllers for the optimal control problem with the finite horizon.
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