In this paper, we consider a control synthesis problem for a class of polynomial dynamical systems subject to bounded disturbances andwith input constraints. More precisely, we aim at synthesizing at the same time a controller and an invariant set for the controlled system under all admissible disturbances. We propose a computational method to solve this problem. Given a candidate polyhedral in...

Using hybrid automata, one is able to model many types of systems and express their properties in various formal languages. Being extremely general and rich, however, the class of hybrid automata exhibits the inherent problems of automata theory: even the simplest of properties for general hybrid automata are undecidable. Therefore, one must restrict attention only to subclasses of this very ge...

We study the Witten–Reshetikhin–Turaev SU(2) invariant for the Seifert manifold S/Γ where Γ is a finite subgroup of SU(2). We show that the WRT invariants can be written in terms of the Eichler integral of the modular forms with half-integral weight, and we give an exact asymptotic expansion of the invariants by use of the nearly modular property of the Eichler integral. We further discuss that...

In this paper, based on algebraic arguments, a new proof of the spectral characterization of those real matrices that leave a proper polyhedral cone invariant [Trans. Amer. Math. Soc., 343 (1994), pp. 479–524] is given. The proof is a constructive one, as it allows us to explicitly obtain for every matrix A, which satisfies the aforementioned spectral requirements, an A-invariant proper polyhed...

We study the Witten–Reshetikhin–Turaev SU(2) invariant for the Seifert manifolds S/Γ where Γ is a finite subgroup of SU(2). We show that the WRT invariants can be written in terms of the Eichler integral of modular forms with half-integral weight, and we give an exact asymptotic expansion of the invariants by use of the nearly modular property of the Eichler integral. We further discuss that th...

Zeno hybrid automata are hybrid systems that can exhibit in nitely many discrete transitions in a nite time interval. Such automata arise due to modeling simplications and may deteriorate simulation e ciency and accuracy considerably. Some basic properties of Zeno hybrid automata are explored. Possible ways to extend a simulation beyond the Zeno time are suggested.

Necessary and su cient conditions for hybrid automata to be non-blocking and deterministic (local existence and uniqueness of executions, respectively) are developed. The problem of global existence of executions is discussed in the context of Zeno hybrid automata, that is, hybrid automata that can exhibit in nitely many discrete transitions in nite time.