Robust Controller Design for Polytopic Systems via Robust Elimination Lemma

appear in the study of robust stability conditions for linear systems with polytopic uncertainties [2], [7]. The matrices Gi, Ui, Vi and X all may depend on the control system parameters to be designed. In some cases the matrix X prevents an immediate application of control design procedures and should be eliminated from inequality (1), thus eliminating some parameters and simplifying the design inequalities. The following linear algebra result, known as Elimination Lemma can be used to eliminate the matrix X from the inequalities (1) if N = 1 [1], [8].