Design of an observer for quantized output systems using orthogonal projection

This paper presents a state observer for linear systems with quantized outp uts. The observer employs an orthogonal projection operation at quantizer o utput 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 e rror. 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 pro jection operation in the proposed observer, the simple motor system with an optical encoder has been analyzed numerically.