On the Markov property of quantised state measurement sequences

This paper is concerned with the representation of stable autonomous discre te-time systems with quantised state measurements. It is assumed that the s tate space R" is partitioned into disjoint regions 2(x) which are enumerate d. Only the number z(k) of the region 2(x) to which the state x(k) belongs can be measured. As a consequence, the initial state x(0) is an element of R" is unknown and assumed to be uniformly distributed over the set 2(x)(z(0 )) associated with the measurement z(0). The paper shows that the measureme nt sequence z(k) (k = 0, 1, ...) is, in general, not a Markov chain. Hence, the sequence of probability distributions cannot be represented exactly by a stochastic automaton whose state set equals the set of measurement symbo ls. (C) 1998 Elsevier Science Ltd. All rights reserved.