Qualitative modelling of linear dynamical systems with quantized state measurements

Abstract The paper considers a discrete-time continuous-variable autonomous system for which only a quantized state measurement [ x (k) ] is available. The problem is to set up a qualitative model that for a given quantized initial state [x(0)] describes the sequence of quantized states [ x (k) ]. First it is shown that the relation between [x(0)] and [ x (k) ] is ambiguous. Hence, the qualitative model is nondeterministic. Second, necessary and sufficient conditions are derived under which nondeterministic or stochastic automata represent qualitative models of a linear autonomous system. The results are illustrated by an oscillator.

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