A note on `Families of linear-quadratic problems: continuity properties´

In the above-mentioned paper by H.L. Trentelman (see ibid vol. AC-32, pp.323-329, 1987), one-parameter (ε) families of these problems with stability are investigated. It is shown that the set of invariant zeros of the ε-problem is contained in the set of invariant zeros of the boundary problem (the problem with ε=0) if the boundary system is left invertible. This result is obtained by applying only the assumptions on the continuity and the monotonicity of the weighting matrices that are made in the above-mentioned paper. Consequently, one can replace the third assumption in that paper by a much weaker one