Irreducibles and the composed product for polynomials over a finite field
Discrete Mathematics
Reachability analysis of dynamical systems having piecewise-constant derivatives
Theoretical Computer Science - Special issue on hybrid systems
A course in computational algebraic number theory
A course in computational algebraic number theory
Widening the Boundary between Decidable and Undecidable Hybrid Systems
CONCUR '02 Proceedings of the 13th International Conference on Concurrency Theory
On the Decidability of the Reachability Problem for Planar Differential Inclusions
HSCC '01 Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control
Modern Computer Algebra
Robust simulations of turing machines with analytic maps and flows
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
Survey A survey of computational complexity results in systems and control
Automatica (Journal of IFAC)
Invariants for LTI systems with uncertain input
RP'12 Proceedings of the 6th international conference on Reachability Problems
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Dynamical systems allow to modelize various phenomena or processes by only describing their way of evolution. It is an important matter to study the global and the limit behaviour of such systems. A possible description of this limit behaviour is via the omega-limit set: the set of points that can be limit of subtrajectories. The omega-limit set is in general uncomputable. It can be a set highly difficult to apprehend. Some systems have for example a fractal omega-limit set. However, in some specific cases, this set can be computed. This problem is important to verify properties of dynamical systems, in particular to predict its collapse or its infinite expansion. We prove in this paper that for linear continuous time dynamical systems, it is in fact computable. More, we also prove that the 茂戮驴-limit set is a semi-algebraic set. The algorithm to compute this set can easily be derived from this proof.