A Novel Qualitative State Observer

The state estimation of a quantized system (Q.S.) is a challenging problem for designing feedback control and model-based fault diagnosis algorithms. The core of a Q.S. is a continuous variable system whose inputs and outputs are represented by their corresponding quantized values. This paper concerns with state estimation of a Q.S. by a qualitative observer. The presented observer in this paper uses a non-deterministic automaton as its qualitative model and estimates quantized values of the system state. Observer inputs are on-line measured input and output signals of Q.S. The previous proposed qualitative observers use dynamics of the continuous variable system of Q.S., whereas, in this paper, the qualitative observer model is built by a quantitative observer. The main theorem of the paper shows that if the parameters of quantitative observer and sampling time are chosen correctly, then qualitative estimation error will be uniformly ultimate bounded, i.e. it will converge to a bounded convex set. In addition, simulation results show that reducing bounds of the convex set results in less additional generated spurious states.