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In this work, by using a generalized Halanay inequality, a regular Lyapunov function and the theory of nonsmooth analysis, we investigate the uniformly ultimate boundedness of the zero solution for nonautonomous delay differential inclusions. The ...

In this paper, we develop an enhanced version of the catching-up algorithm for sweeping processes through an appropriate concept of approximate projection. We establish some properties of this notion of approximate projection. Then, under suitable ...

In this article, we study a class of differential quasi-variational–hemivariational inequalities involving time delays. We establish new systems and prove the solvability and the existence of decay solutions. Moreover, we are concerned with long-...

We consider first-order methods with constant step size for minimizing locally Lipschitz coercive functions that are tame in an o-minimal structure on the real field. We prove that if the method is approximated by subgradient trajectories, then ...

We consider differential inclusions with strengthened one-sided Lipschitz (SOSL) right-hand sides. The class of SOSL multivalued maps is wider than the class of Lipschitz ones and a subclass of the class of one-sided Lipschitz maps. We prove a ...$\frac{\mathrm{}}{\mathrm{}}$

In this paper we consider the problem of determining the stability properties, and in particular assessing the exponential stability, of a singularly perturbed linear switching system. One of the challenges of this problem arises from ...

We consider the subgradient method with constant step size for minimizing locally Lipschitz semi-algebraic functions. In order to analyze the behavior of its iterates in the vicinity of a local minimum, we introduce a notion of discrete Lyapunov ...

We consider the Volterra integro-differential equation with a time-dependent prox-regular constraint that changes in an absolutely continuous way in time (a Volterra absolutely continuous time-dependent sweeping process). The aim of our paper is ...

In this article, we derive first-order necessary optimality conditions for a constrained optimal control problem formulated in the Wasserstein space of probability measures. To this end, we introduce a new notion of localised metric ...

For finite-dimensional problems, stochastic approximation methods have long been used to solve stochastic optimization problems. Their application to infinite-dimensional problems is less understood, particularly for nonconvex objectives. This ...${}^{\mathrm{}}$

The standard theory of stochastic approximation (SA) is extended to the case when the constraint set is a Riemannian manifold. Specifically, the standard ODE method for analyzing SA schemes is extended to iterations constrained to stay on a ...

This paper is concerned with finite-time and fixed-time synchronization of complex-valued recurrent neural networks with discontinuous activations and time-varying delays. First, by separating the complex-valued recurrent neural networks into real ...

The article deals with the stability of discontinuous homogeneous nonlinear systems with aperiodic sampled-data inputs. We first extend results about robustness of homogeneous nonlinear systems to the discontinuous case. Then, we prove ...

In this paper, we study the existence and the stability in the sense of Lyapunov of differential inclusions governed by the normal cone to a given prox-regular set, which is subject to a Lipschitzian perturbation. We prove that such apparently more ...

The term `distance estimate' for state constrained control systems refers to an estimate on the distance of an arbitrary state trajectory from the subset of state trajectories that satisfy a given state constraint. Distance estimates have found ...

This paper is concerned with the problem of passivity and stability analysis for a class of memristor-based neural networks with leakage delay and state-dependent switched memductance functions. By combining differential inclusions with set-valued maps ...

Let X be a real Banach space and I a nonempty interval. Let K:IźX$K:I\rightsquigarrow X$ be a multi-function with the graph K$\mathcal {K} $. We give here a characterization for K$\mathcal {K} $ to be approximate/near weakly invariant with respect to ...

We study the limiting behaviour of stochastic models of populations of interacting agents, as the number of agents goes to infinity. Classical mean-field results have established that this limiting behaviour is described by an ordinary differential ...

This note presents a refinement of Matrosov's theorem for a class of differential inclusions whose set-valued map is defined as a closed convex hull of finitely many vector fields. This class of systems may arise in the analysis of switched nonlinear ...

In this paper, a general framework named Filippov-framework and some new analytic techniques are presented for dealing with the exponential synchronization of memristor-based neural network system with time-varying delay. Several new sufficient ...