Abstract <p> The article is devoted to solving the problem of controlling a system defined by ordinarydifferential equations with a nonlinear right-hand side, which has the property ofquasi-monotonicity with respect to offdiagonal entries. The equations also contain controlparameters and uncertainties (errors), whose possible values must satisfy some pointwiseconstraints. The problem of control over a finite time interval is considered in order to transfer thestate of the system to a given target set. The current state of the system is unknown, and for theformation of a control strategy, only a priori estimates of the initial state are available, as well asthe results of incomplete and inaccurate measurement results received online. To solve theproblem, a well-known general scheme is used, according to which it is necessary to consistentlysolve three subproblems: the approximate construction of information sets of the system,solvability sets, and, finally, the control synthesis problem. In the present paper, this generalscheme is successfully implemented for the special class of nonlinear systems under consideration.Theorems on external interval estimates of information sets, internal estimates of solvability sets,and on sufficient conditions for the solvability of the control problem are proved. Formulas forfeedback control are obtained, depending on the so-called generalized position, formed on the basisof available information about the system and measurement results. The possibility of applyingthe theoretical results obtained to solve specific control problems is confirmed by the modelexample analyzed in the paper.</p>