ON QUALITATIVE BEHAVIOR OF A CLOSED-LOOP

This paper concerns the characterization of qualitative behavior of a closed-loop quantized system. A quantized system is a dynamical system, which instead of knowing its state x(t) and its input u(t) pre-cisely, their qualitative values [x(t)] and [u(t)] at a discrete time set T = {t0, t1, …, tk, …} are known. The qualitative state [x(t)] and the qualitative input [u(t)] are qualitative assessments of their precise values x(t) and u(t) respectively, and they can be related to each other via a non-deterministic automaton description. The aim is to charac-terize the state behavior of a quantized system whenever its non-deterministic automaton description is given. The first result of the paper is derivation of a representation W(k + 1) = AW(k) for a non-deterministic closed-loop automaton. The second result of the paper shows that the state-behavior of a closed-loop quantized system can be characterized according to the eigenvalues of matrix A in a similar manner with usual linear discrete-time systems