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In this paper, a new interval arithmetic approach for analysis and design of robust controllers of systems with bounded state and control variables is presented. Based on guaranteed simulations of nonlinear dynamical systems with uncertain parameters, bounds of the admissible range of the control variables are calculated. During the computation of these bounds, time-dependant restrictions of the state variables arc considered as well as limitations of the control variables. To point out the advantages of this approach, it is applied to a subsystem model of the activated sludge process in biological wastewater treatment describing the reduction of biodegradable organic matter.