Rejection of bounded exogenous disturbances by the method of invariant ellipsoids

Rejection of the bounded exogenous disturbances was first studied by the $l_1$-optimization theory. A new approach to this problem was proposed in the present paper on the basis of the method of invariant ellipsoids where the technique of linear matrix inequalities was the main tool. Consideration was given to the continuous and discrete variants of the problem. Control of the “double pendulum” was studied by way of example.