Hybrid automata are a powerful formalism for modeling and verifying hybrid systems, that combine continuous and discrete behavior. A common problem for hybrid systems is the good parameters problem, which consists in identifying a set of parameter valuations guaranteeing a certain good behavior of a system. We introduce here HyMITATOR, a tool for efficient parameter synthesis for hybrid automat...

Revisiting the notion of μ-almost equicontinuous cellular automata introduced by R. Gilman, we show that the sequence of image measures of a shift ergodic measure μ by iterations of a μ-almost equicontinuous cellular automata F , converges in Cesaro mean to an invariant measure μc. If the initial measure μ is a Bernouilli measure, we prove that the Cesaro mean limit measure μc is shift mixing. ...

Revisiting the notion of μ-almost equicontinuous cellular automata introduced by R. Gilman, we show that the sequence of image measures of a shift ergodic measure μ by iterations of such automata converges in Cesaro mean to an invariant measure μc. If the initial measure μ is a Bernouilli measure, we prove that the Cesaro mean limit measure μc is shift mixing. Therefore we also show that for an...

Revisiting the notion of μ-almost equicontinuous cellular automata introduced by R. Gilman, we show that the sequence of image measures of a shift ergodic measure μ by iterations of a μ-almost equicontinuous cellular automata F , converges in Cesaro mean to an invariant measure μc. If the initial measure μ is a Bernouilli measure, we prove that the Cesaro mean limit measure μc is shift mixing. ...

A hybrid system is a dynamical system whose behavior exhibits both discrete and continuous change. A hybrid automaton is a mathematical model for hybrid systems, which combines, in a single formalism, automaton transitions for capturing discrete change with di erential equations for capturing continuous change. In this survey, we demonstrate symbolic algorithms for the veri cation and controlle...

We discuss a close link between two seemingly different topics studied in the cellular automata literature: additive conservation laws and invariant probability measures. We provide an elementary proof of a simple correspondence between invariant full-support Bernoulli measures and interaction-free conserved quantities in the case of onedimensional surjective cellular automata. We also discuss ...

Reversible cellular automata are seen as microscopic physical models, and their states of macroscopic equilibrium are described using invariant probability measures. Characterizing all the invariant measures of a cellular automaton could be challenging. Nevertheless, we establish a connection between the invariance of Gibbs measures (used in statistical mechanics to describe thermodynamic equil...

Hybrid integrator–gain systems (HIGS) are nonlinear elements designed for overcoming fundamental limitations of linear time-invariant integrators. This paper presents numerically robust conditions time-domain stability and performance HIGS-controlled systems. In particular, using piecewise quadratic (PWQ) Lyapunov functions defined over polyhedral subregions the state-space, computations upper-...