Adaptive Stabilization of Linear Systems Through a Two-Way Channel with Limited Capacity

The paper is devoted to adaptive feedback stabilization for linear time-invariant control systems with saturated quantized measurements and control. The quantization occurs due to the finite capacity of the discrete-time two-way channel connecting the plant and the controller. An adaptive controller based on the Yakubovich’s recursive goal inequalities method is designed. The bound for the minimum channel capacity sufficient to stabilize any stabilizable system with unknown parameters is evaluated for any prespecified compact set of unknown parameters.