Optimal control for a singularly perturbed linear stochastic system with multiplicative white noise perturbations and Markovian jumping

In this study, we investigate the optimal control of a class of singularly perturbed linear stochastic systems with Markovian jumping parameters. After establishing an asymptotic structure for the stabilizing solution of the coupled stochastic algebraic Riccati equations, a parameter‐independent composite controller is derived. Furthermore, the cost degradation in a reduced‐order controller is discussed. Thus, the exactness of the proposed approximate control is discussed for the first time. As an additional important contribution, a numerical algorithm for solving the coupled stochastic algebraic Riccati equations is proposed, and the feature of the resulting higher‐order controller is shown. Finally, a simple example is presented to demonstrate the validity of the proposed method.