Asymptotic stabilization of continuous-time linear systems with quantized state feedback

This paper considers an asymptotic stabilization problem of continuous-time linear systems subject to state quantization. Based on spherical polar coordinates, a quantizer is proposed with a desired relation between the quantized data and the corresponding quantization error for this problem. Owing to the quantization error the resulting closed-loop system is described by a discontinuous right-hand side differential equation and the notion of Krasovskii solution is adopted for the equation. By the proposed quantizer, a time-invariant coding scheme is first proposed and further a state feedback controller is designed to achieve convergence of the closed-loop trajectories toward a compact surface surrounding the origin, on which sliding motion occurs. Then, a time-varying coding scheme is proposed to avoid chattering phenomena induced by the sliding motion on the surface and achieve asymptotic stability of systems.