Impulse differential inclusions are introduced as a framework for modeling hybrid phenomena. Connections to standard problems in the area of hybrid systems are discussed. Conditions are derived that allow one to determine whether a set of states is viable or invariant under the action of an impulse differential inclusion. For sets that violate these conditions, methods are developed for approxi...

Proof: 2 L(H D) (2 L(H C)) provided there is a sequence =< D(l 0); 0 ; 0 >< D(l 1); 1 ; 1 > : : : which is discrete-time (continuous-time) consistent. As discussed at beginning of Sect. 3, every discrete-time consistent sequence is continuous-time consistent. From Lemma 3-Lemma 7, every continuous-time consistent sequence is also discrete-time consistent. Thus 2 L(H D) i 2 L(H C). Theorem 9. L(...

In this paper we deal with a class of non-differentiable functionals defined on a real reflexive Banach space X and depending on a real parameter of the form Eλ(u) = L(u)− (J1 ◦T )(u)−λ(J2 ◦ S)(u), where L : X → R is a sequentially weakly lower semicontinuous C functional, J1 : Y → R, J2 : Z → R (Y, Z Banach spaces) are two locally Lipschitz functionals, T : X → Y , S : X → Z are linear and com...

Formulations of fuzzy integral equations in terms of the Aumann integral do not reflect the behavior of corresponding crisp models. Consequently, they are ill-adapted to describe physical phenomena, even when vagueness and uncertainty are present. A similar situation for fuzzy ODEs has been obviated by interpretation in terms of families of differential inclusions. The paper extends this formal...

In this articlewe discuss the differential inclusion known as state dependent sweeping process for a class of prox-regular non-convex sets.We associate with any state dependent sweeping process with such sets an unconstraint differential inclusion whose any solution is a solution of the state sweeping process too. We prove a theorem on the existence of a global solution of nonconvex state depen...

The paper is concerned with the non-autonomous ordinary differential inclusion in finite dimensional space with periodic, compact, but not necessarily convex valued right-hand side. The existence of periodic solution for such an inclusion which stays in a strongly positively invariant (under inclusion) set continuously depending on the time parameter is proved. The connection between the densit...

The paper studies controllability problems for the reachable set of a differential inclusion. These were originally motivated by models of control of a flock of animals. Conditions are derived for the existence or nonexistence of a strategy which confines the reachable set within a given bounded region, at all sufficiently large times. Steering problems and the asymptotic shape of the reachable...

In this paper, a hyperbolic differential inclusion with nonmonotone discontinuous and nonlinear term, which the generalized velocity acts as its variable, is studied and the existence and decay of its weak solution are obtained.

This paper presents an approach to handle some problems arising in the modelling of hybrid systems combining static and dynamic. In the case of a discrete or continuous dynamic system, there is no particular condition forcing a solution of a differential inclusion starting from a point x0 to remain in a set K defined by a set of static constraints. We study the subsets of K containing only the ...

We consider a Cauchy problem for a Sturm-Liouville type differential inclusion involving a nonconvex set-valued map and we prove that the set of selections corresponding to the solutions of the problem considered is a retract of the space of integrable functions on unbounded interval.