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Parallelograms inscribed in a curve having a circle as π/2-isoptic

Andrzej Miernowski (2008)

Annales UMCS, Mathematica

Jean-Marc Richard observed in [7] that maximal perimeter of a parallelogram inscribed in a given ellipse can be realized by a parallelogram with one vertex at any prescribed point of ellipse. Alain Connes and Don Zagier gave in [4] probably the most elementary proof of this property of ellipse. Another proof can be found in [1]. In this note we prove that closed, convex curves having circles as π/2-isoptics have the similar property.

Sliding subspace design based on linear matrix inequalities

Alán Tapia, Raymundo Márquez, Miguel Bernal, Joaquín Cortez (2014)

Kybernetika

In this work, an alternative for sliding surface design based on linear and bilinear matrix inequalities is proposed. The methodology applies for reduced and integral sliding mode control, both continuous- and discrete-time; it takes advantage of the Finsler's lemma to provide a greater degree of freedom than existing approaches for sliding subspace design. The sliding surfaces thus constructed are systematically found via convex optimization techniques, which are efficiently implemented in commercially...

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