The article presents conditions under which the probability of a linear combination random vectors falling into polyhedral cone is Schur-concave function coefficients combination. It required that contains point 0, its edges are parallel to coordinate axes, and distribution density logarithmically concave sign-invariant function.

Motivated by an example from aircraft connict resolution we seek a methodology for synthesizing controllers for nonlinear hybrid automata. We rst show how game theoretic methodologies developed for this purpose for nite automata and continuous systems can be cast in a uniied framework. We then present a conceptual algorithm for extending them to the hybrid setting. We conclude with a discussion...

Slope-parametric hybrid automata (SPHA) are hybrid automata whose variables can have parametric slopes. SPHA are useful, in particular, for modeling task-control systems in which the task speeds can be adjusted for meeting some safety requirement. In this paper, we present an example of parametric analysis for a simple task system. We introduce a prototype veriication tool that fully automates ...

We present a method to estimate the domain of attraction of a class of discretetime Lur’e systems. A new notion of LNL-invariance, stronger than the traditional invariance concept, is introduced. An algorithm to determinate the largest LNL-invariant set for this class of systems is proposed. Moreover, it is proven that the LNL-invariant sets provided by this algorithm are polyhedral convex sets...

We present a formalism for modular modeling of hybrid systems, the Cottbus Timed Automata. For the theoretical basis, we build on work about timed and hybrid automata. We use concepts from concurrency theory to model communication of separately defined modules, and we extend these concepts to be able to express explicitly readand write-access to signals and variables.

This draft suggests a new counterexample guided abstraction refinement (CEGAR) framework that uses the combination of numerical simulation for nonlinear differential equations with linear programming for linear hybrid automata (LHA) to perform reachability analysis on nonlinear hybrid automata. A notion of ǫ− structural robustness is also introduced which allows the algorithm to validate counte...

We present a formalism for modular modelling of hybrid systems, the Cottbus Timed Automata. For the theoretical basis, we build on work about timed and hybrid automata. We use concepts from concurrency theory to model communication of separately defined modules, but we extend these concepts to be able to express explicitly readand write-access to signals and variables.

Abstract We show that the pseudoeffective cone of k -cycles on a complete complexity-one T -variety is rational polyhedral for any , generated by classes -invariant subvarieties. When X also rational, we give presentation Chow groups in terms generators and relations, coming from combinatorial data defining as -variety.