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This note is concerned with conditions on a set of non-singular matrices A i ∈ R n × n , i = 1 , 2 , ... , r , so that any convex combination of these matrices is also non-singular. The first part of the note points out that Theorem 2.3 in a previous paper [Beteto et al. (2021). Less conservative conditions for robust LQR-state derivative controller design: An LMI approach. International Journal of Systems Science] provides only necessary conditions, which are not sufficient in the general case. In the second part, some stability results based on Linear Matrix Inequalities (LMIs) for a class of fractional order systems are used to establish new sufficient conditions. Numerical examples are presented for illustration. The results suggest that the new LMI conditions may be less conservative compared to a test proposed in the literature on P-matrices, and also to a positive-definiteness test based on matrix cross-products. [ABSTRACT FROM AUTHOR]

The article focuses on various aspects of territorial cooperation process in Europe. It mentions need for spreading experience of the European Grouping of Territorial Cooperation (EGTC) across all European Union (EU) borders. It states need for conducting academic research with regard to European Territorial Cooperation and need for implementing longer-term cross-border planning process.

The article discusses the early career Master Class hosted by European Commission's DG for Regional and Urban Policy and the Committee of the Regions held from October 6 to October 8, 2014 on future research on European Union Cohesion Policy. It mentions need for research to focus on possibilities to reduce political intervention in public administrations and role of civil society organizations. It states need for a longer-term cross-border planning process according to Marco Trienes.