Let P be a lattice polytope with the $$h^{*}$$ -vector $$(1, h^*_1, \ldots , h^*_s)$$ . In this note we show that if $$h_s^* \le h_1^*$$ then Ehrhart ring $${\mathbb {k}}[P]$$ is generated in degrees at most $$s-1$$ as {k}}$$ -algebra. particular, $$s=2$$ and $$h_2^* IDP. To see this, corresponding statement for semi-standard graded Cohen–Macaulay domains over algebraically closed fields.

In this paper, we extend the decomposable systems framework to multi-agent with Bernoulli distributed packet loss uniform probability. The proposed sufficient analysis conditions for mean-square stability and $H_2$-performance -- which are expressed in form of linear matrix inequalities scale linearly increased network size thus allow analyse even very large-scale systems. A numerical example d...

This paper provides new insights into the currently available extended linear matrix inequality (LMI) conditions for control of discrete-time linear systems, motivating the use of two intrinsically different extended LMI characterizations for H2 performance. While these conditions are equivalent for H2 analysis and many H2 control problems related to precisely known linear time-invariant (LTI) ...

We continue a recent systematic study into the clique-width of (H1, H2)-free graphs and present five new classes of (H1, H2)-free graphs of bounded clique-width. As a consequence, we have reduced the number of open cases from 13 to 8. Four of the five new graph classes have in common that one of their two forbidden induced subgraphs is the triangle. As such, we generalize corresponding results ...