An Extended Martingale Invariance Principle

Extended LaSalle's Invariance Principle for Full-Range Cellular Neural Networks

In several relevant applications to the solution of signal processing tasks in real time, a cellular neural network (CNN) is required to be convergent, that is, each solution should tend toward some equilibrium point. The paper develops a Lyapunov method, which is based on a generalized version of LaSalle’s invariance principle, for studying convergence and stability of the differential inclusi...

An extended variational principle

An invariance principle for random planar maps

We show a new invariance principle for the radius and other functionals of a class of conditioned ‘Boltzmann-Gibbs’distributed random planar maps. It improves over the more restrictive case of bipartite maps that was discussed in Marckert and Miermont (2006). As in the latter paper, we make use of a bijection between planar maps and a class of labelled multitype trees, due to Bouttier et al. (2...

An Invariance Principle for Conditioned Trees

We consider Galton-Watson trees associated with a critical offspring distribution and conditioned to have exactly n vertices. These trees are embedded in the real line by affecting spatial positions to the vertices, in such a way that the increments of the spatial positions along edges of the tree are independent variables distributed according to a symmetric probability distribution on the rea...

An invariance principle for nonlinear switched systems

In this paper we address the problem of extending La Salle Invariance Principle to switched system. We prove an extension of the invariance principle relative to dwell-time switched solutions, and a second one relative to constrained switched systems.