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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.

This paper presents a state observer for linear systems with quantized outputs. The observer employs an orthogonal projection operation at quantizer output discontinuities to enhance its convergence rate for quantized output systems. Although there may be a significant quantization error on average, it is possible to design observers with an exponentially stable tracking error. We explain how to construct the orthogonal projection operation in a Hilbert space and prove the stability of the proposed observer by using the Lyapunov second method. In order to assess the value of the orthogonal projection operation in the proposed observer, the simple motor system with an optical encoder has been analyzed numerically.

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