Near optimal linear quadratic regulator for a singularly perturbed linear stochastic system with multiplicative white noise perturbations and Markovian jumping

We study the optimal control of a class of singularly perturbed linear stochastic systems (SPLSS) with Markovian jumping parameters. After establishing an asymptotic structure for the stabilizing solution of the coupled stochastic algebraic Riccati equations (CSAREs), a parameter-independent composite controller is derived. Furthermore, the cost degradation in a reduced-order controller is also discussed.