International audienceNumerical methods are necessary to understand the behav- iors of complex hybrid systems used to design control-command systems. Especially, numerical integration methods are heavily used in simulation to compute approximations of the solution of differential equations, in- cluding non-linear and stiff solutions. Nevertheless, these methods only produce approximate results and they should not be used in formal ver- ification methods as is. We propose a systematic way to make explicit Runge-Kutta integration method safe with respect to the mathemati- cal solution. As side effect, we can hence compare different integration schemes in order to pick the right one in different situations

International audienceThe industrial tool Matlab/Simulink is widely used in the design of embedded systems. The main feature of this tool is its ability to model in a common formalism the software and its physical environment. This makes it very useful for validating the design of embedded software using numerical simulation. However, the formal verification of such models is still problematic as Simulink is a programming language for which no formal semantics exists. In this article, we present an operational semantics of a representative subset of Simulink which includes both continuous-time and discrete-time blocks. We believe that this work gives a better understanding of Simulink and it defines the foundations of a general framework to apply formal methods on Simulink's high level descriptions of embedded systems

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Recently, barrier certificates have been introduced to prove the safety of continuous or hybrid dynamical systems. A barrier certificate needs to exhibit some barrier function, which partitions the state space in two subsets: the safe subset in which the state can be proved to remain and the complementary subset containing some unsafe region. This approach does not require any reachability analysis, but needs the computation of a valid barrier function, which is difficult when considering general nonlinear systems and barriers. This paper presents a new approach for the construction of barrier functions for nonlinear dynamical systems. The proposed technique searches for the parameters of a parametric barrier function using interval analysis. Complex dynamics can be considered without needing any relaxation of the constraints to be satisfied by the barrier function.