In the paper we study the continuity properties of the solution set of upper semicontinuous differential inclusions in both regularly and singularly perturbed case. Using a kind of dissipative type of conditions introduced in [1] we obtain lower semicontinuous dependence of the solution sets. Moreover new existence result for lower semicontinuous differential inclusions is proved.

Using the notion of continuous approximate selections , we establish an existence theorem for set differential inclusions in a semi-linear metric space.

The problem of detectability of inclusions by boundary measurements is considered. The inclusions diier from the background material by their conductivity, the location of inclusions is unknown. The detectability is equal to the diierence of energies needed to inject currents in the model body without inclusion and in the sample under investigation. We consider a game where inclusions hide in t...

The notion of geometric homogeneity is extended for differential inclusions. This kind of homogeneity provides the most advanced coordinate-free framework for analysis and synthesis of nonlinear discontinuous systems. The main qualitative properties of continuous homogeneous systems are extended to the discontinuous setting: the equivalence of the global asymptotic stability and the existence o...

This article addresses the problem of stability of impulsive control systems whose dynamics are given by measure driven differential inclusions. One important feature concerns the adopted solution which allows the consideration of systems whose singular dynamics do not satisfy the so-called Frobenius condition. After extending the conventional notion of control Lyapounov pair for impulsive syst...

We establish some sufficient conditions in order that a given locally closed subset of a separable Banach space be a viable domain for a semilinear functional differential inclusion, using a tangency condition involving a semigroup generated by a linear operator.

This article is dedicated to Jean Jacques Moreau for his 80th birthday. He is a master of convex analysis. When dealing with differential inclusions of the form Du (x) ∈ E, a.e. in Ω together with some boundary data u = φ on ∂Ω, one is lead to consider several types of convex hulls of sets. It is the aim of the present article to discuss these matters.

In this paper we prove the existence of solutions to the following third order differential inclusion:  x(3)(t) ∈ F (t, x(t), ẋ(t), ẍ(t)) + G(x(t), ẋ(t), ẍ(t)), a.e. on [0, T ] x(0) = x0, ẋ(0) = u0, ẍ(0) = v0, and ẍ(t) ∈ S,∀t ∈ [0, T ], where F : [0, T ]×H×H×H → H is a continuous set-valued mapping, G : H× H × H → H is an upper semi-continuous set-valued mapping with G(x, y, z) ⊂ ∂g(z) where g...

The non-autonomous bouncing ball system consists of a point mass m in a constant gravitational field g, which bounces inelastically on a flat vibrating table. The presented Lyapunov-like method is set up for non-autonomous measure differential inclusions and constructs a decreasing step function W above the oscillating Lyapunov function V . Furthermore, it is proven that the attractivity of the...

In the paper, we study weak invariance of differential inclusions with non-fixed time impulses under compactness type assumptions. When the right-hand side is one sided Lipschitz an extension of the well known relaxation theorem is proved. In this case also necessary and sufficient condition for strong invariance of upper semi continuous systems are obtained. Some properties of the solution set...