Control for Multiplicative Noise Systems With Packet Losses and Measurement Delays

This paper mainly considers the control problems for discrete-time multiplicative noise systems with packet losses and measurement delays. The main contributions are two-fold. Firstly, based on Pontryagin's maximum principle, the optimal output feedback controller is obtained. Secondly, a necessary and sufficient stabilization condition for multiplicative noise systems is derived in terms of the coupled algebraic Riccati equations. Moreover, it has been proved that the stabilization condition only depends on the eigenvalue of the system matrix and the probability of packet losses which is not related to measurement delays.