Mean-Square Stabilizability for Output Feedback Control under Quantization Constraints

This paper studies the stability problem of linear time-invariant (LTI), single-input single-output (SISO) discrete-time network control systems with quantization constraints on control signal. The logarithmic quantizer is considered and we want to design an output-feedback controller to make the closed-loop system be mean-square stability. In this process, the output-feedback controller is realized by Youla parameterization. A sufficient and necessary condition is receive to guarantee the mean-square stability of closed-loop system which is determined by the unstable poles of given systems and the unique solutions to two algebraic Riccati equations. Specially, this sufficient and necessary condition is only depended on the plant unstable poles for minimum phase plant case. These results also provide an output feedback controller design method to stabilize a linear system with multiplicative noise.