Asymptotic stabilisation of system with finite-level logarithmic quantiser

A quantised feedback control for the asymptotic stabilisation of a system with a finite-level logarithmic quantiser is proposed. The main idea is to employ one from among the current, upper and lower quantising levels as the quantised input to maintain the decreasing property of a Lyapunov function. The resulting controller allows for an arbitrarily small quantisation density, whereas existing controllers in the literature do not, in the finite-level logarithmic quantiser for asymptotic stabilisation.