Simultaneous state and parameter estimation of nonlinear discrete-time systems is addressed. The developed procedure is dedicated to Multiple-Input-Multiple-Output (MIMO) bounded-state nonlinear systems subject to either linear or nonlinear parametrization. It is shown that under the persistent excitation condition the unmeasured states along with the system parameters can be reproduced asymptotically if the upper and the lower bounds of the system states are assumed to be known. The existence of the observer gain is conditioned by the solvability of a linear matrix inequality (LMI). Simulation results are provided to highlight the efficacy of the developed theoretical results. Published by Elsevier Ltd.