In this paper, first the mathematical models of four major environmental disturbance torque components and corresponding bound equations are presented. Then the effect of the inertia matrix uncertainty on rigid satellite's attitude dynamics is defined as an external torque in the derived state equation, which together with environmental torques forms the so-called lumped disturbance torque. After obtaining the complete equation for the model uncertainty-induced torque vector, its exact bound equation is derived by using matrix-vector norm relations. To validate the significance of these preliminary results for use in robust attitude controller design, a new modification of the classical sliding mode attitude controller present in literature is proposed, which is the primary contribution of this paper. The new design that is based on comprehensive knowledge of the lumped disturbance's bounded variation leads to a decision rule on the switching control gain that is not excessively conservative. After verifying the accuracy of the bound equations in a simulation under no control, a second simulation is carried out with control input from the designed sliding mode controller to show that the proposed design works. The superiority of the new design is discussed in comparison with another design from literature that does not exploit the complete model of the inertia matrix uncertainty-induced torque through a comparative simulation's result. The conclusion is that the modified controller design results in an attitude control system that has guaranteed robust stability in addition to reasonable conservativeness thanks to the newly obtained comprehensive decision rule on the switching control gain. (C) 2017 American Society of Civil Engineers.