This paper deals with state observer design problem for a class of nonlinear dynamical systems with interval time-varying delay that satisfies the one-sided Lipschitz condition. The systems under consideration include the well-studied Lipschitz system as a special case and possess inherent advantages with respect to conservativeness. By constructing a novel Lyapunov-Krasovskii functional and ut...

In the given study, we investigate three-step NTS’s ball convergence for solving nonlinear operator equations with a order of five in Banach setting. A operator’s first-order derivative is assumed to meet generalized Lipschitz condition, also known as κ-average condition. Furthermore, several theorems on same method spaces are developed conditions that operators must satisfy radius or center-Li...

In this paper‎, ‎we introduce and study some new single-valued gap functions for non-differentiable semi-infinite multiobjective optimization problems with locally Lipschitz data‎. ‎Since one of the fundamental properties of gap function for optimization problems is its abilities in characterizing the solutions of the problem in question‎, ‎then the essential properties of the newly introduced ...

We provide a Poincaré inequality for families of Lipschitz continuous vector fields satisfying a Hörmander-type condition of step two.

Iterative learning control methods are represented as powerful tools to control dynamics nowadays. Our new controller based on particular case of iterative learning control is radically different from the presented conventional method, which attempts to stabilize a class of nonlinear systems by satisfying the conditions of Lyapunov Stability Theorem. Since our algorithm is model based, its robu...

We consider metric measure spaces satisfing a doubling condition and a Poincaré inequality in the upper gradient sense. We show that the results of [Che99] on differentiability of real valued Lipschitz functions and the resulting bi-Lipschitz nonembedding theorems for finite dimensional vector space targets extend to Banach space targets having what we term a good finite dimensional approximati...

Fr echet diierentiability of the solution of the heat equation with respect to a nonlinear boundary condition Arnd RR osch Abstract. Consider the heat equation with a nonlinear function in the boundary condition which depends only on the boundary values x of the solution u of the initial-boundary value problem. The function belongs to a set of admissible diierentiable or uniformly Lipschitz con...

In this paper we study the class of differential variational inequality(DVI) in a finite-dimension Euclidean space <n, which is the following form ẋ(t) = f(t, x(t)) + B(t, x(t))u(t) , x(0) = x0 ∈ <n 0 ≤ (ũ− u(t))T [G(t, x(t)) + F (u(t))] for almost all ũ ∈ K u(t) ∈ K We study stability and perturbation of the DVI under the OSL condition. Besides, we establish a Prior Bound Theorem, which is a u...

This paper is concerned with the stability of nonlinear Lipschitz systems subject to bounded process and measurement noises when transmission from sensor to controller is subject to distortion due to quantization. A stabilizing technique and a sufficient condition relating transmission rate to Lipschitz coefficients are presented for almost sure asymptotic bounded stability of nonlinear uncerta...

We study the global attractors of abstract semilinear parabolic equations and their projections to finite-dimensional planes. It is well-known that the attractor can be embedded into the finite-dimensional inertial manifold if the so-called spectral gap condition is satisfied. We show that in the case when the spectral gap condition is violated, it is possible to construct the nonlinearity in s...