State Observer for Linear Time-Invariant Systems With Quantized Output

Abstract

In this paper we introduce a state observer for linear time-invariant systems with quantized outputs. The observer employs an orthogonal projection operation at quantizer output discontinuities to enhance its convergence rate for stable systems. The increasing rate of convergence and stability has been proven by using Lyapunov second method. Some sufficient and necessary conditions of stability for the unstable systems are derived. The sufficient condition of noise stability is given and the maximal bound of noise stability is presented. The proposed methodology has been applied to state estimation of a DC-motor with optical encoder.