Abstract <p>The problem of rejection of linearly bounded exogenous disturbances, i.e., those growing no faster than a linear function of the system state, is considered for linear control systems. The performance is characterized by the size of the bounding ellipsoid containing the system output. A systematic approach to solving this problem is proposed; it reduces the initial problem to an equivalent parameterized semidefinite programming problem, easily solved numerically. It is based on the technique of linear matrix inequalities and the method of invariant ellipsoids. The efficiency of the proposed procedure is demonstrated using a test example.</p>