New Type Of Stability Research Articles

An investigation of factors affecting Fast-Interaction Converter-driven stability in Microgrids

Massive integration of power electronic devices with multiple control schemes in a wide frequency range pose new challenges regarding systems stability and reliability. Interactions between the fast control loops or between the fast control loops and passive elements of the grid, have been reported in literature and have led to introducing a new type of stability: the Fast-Interaction Converter-driven Stability (FICDS). In this paper, factors affecting the FICDS, such as tuning controller parameters, line parameters, number of interconnected inverters, are explored in four microgrid topologies, operating in grid connected and islanded mode. With the use of an impedance based model which tracks the poles of the CDS transfer functions of each system, their stability has been assessed. The obtained results have been verified via time-domain simulations. Simulations from the islanded microgrid of Gaidouromantra in Greece showcase the impact of the control parameters on the operation of the system and indicate the need for further investigation.

A generalization of practical stability of nonlinear impulsive systems

Abstract In this paper, we introduce a new type of stability for nonlinear impulsive systems of differential equations, namely practical h-stability. By using the Lyapunov stability theory, some sufficient conditions which guarantee practical h-stability are established. Our original results generalize well-known fundamental stability results, practical stability, practical exponential stability and practical asymptotic stability for nonlinear time-varying impulsive systems. Then two classes of nonlinear impulsive systems, namely perturbed and cascaded impulsive systems, are discussed. Furthermore, the problem of practical h-stabilization for certain classes of nonlinear impulsive systems is considered. Finally, two numerical examples are given to show the effectiveness of our theoretical results.

A FIXED POINT APPROACH TO STABILITY OF A CUBIC FUNCTIONAL EQUATION IN 2-BANACH SPACES

In this paper, we prove a new type of stability and hyperstability results forthe following cubic functional equationf (2x + y) + f (2x - y) = 2f (x + y) + 2f (x - y) + 12f(x)in 2-Banach spaces using fixed point approach.

Novel tabletop experiment demonstrating the nonlinear resonance excitation observed at the CERN Proton Synchrotron

A compact Paul ion trap is employed to replicate the dynamic behavior of a relativistic charged-particle beam traveling in a large-scale accelerator. The nonlinear resonance bands recently identified at the CERN Proton Synchrotron (PS) are successfully reproduced in the tabletop system. The present experimental data suggests that all these resonances could be excited even without unknown error fields that break the high lattice symmetry of the PS. A new type of stability tune diagram appears to explain the basic feature of the experimental observation.

New stability results for the radical sextic functional equation related to quadratic mappings in $$(2,\beta )$$ ( 2 , β ) -Banach spaces

We first introduce basic concepts of $$(2,\beta )$$ -Banach spaces and we will reformulate the fixed point theorem [8, Theorem 1] in this space. After that, we achieve the general solution of the radical sextic functional equation $$\begin{aligned} f\left( \root 3 \of {x^3+y^3}\right) +f\left( \root 3 \of {x^3-y^3}\right) = 2f(x)+2f(y),\quad x,y\in {\mathbb {R}}, \end{aligned}$$ for f a mapping from the set of all real numbers $${\mathbb {R}}$$ into a vector space. In addition, we prove a new type of stability results for radical sextic functional equation in $$(2,\beta )$$ -Banach spaces. The method is based on a fixed point Theorem 3.1 in some functions spaces.

On a new type of stability of a radical quadratic functional equation using Brzdȩk’s fixed point theorem

Using a fixed point result and an approach to stability of functional equations presented in [8], we investigate a new type of stability for the radical quadratic functional equation of the form $$ f(\sqrt{x^2+y^2}) = f(x) + f(y), $$ where f is a self-mapping on the set of real numbers. We generalize, extend, and complement some earlier classical results concerning the Hyers–Ulam stability for that functional equations.

Global generalized exponential stability for a class of nonautonomous cellular neural networks via generalized Halanay inequalities

This paper investigates a new type of stability, namely global generalized exponential stability of the nonautonomous delayed cellular neural networks. Several novel delay-dependent sufficient conditions are established by applying a new generalized Halanay inequality. In these conditions, the boundedness of time-varying delays and coefficients are not required. In addition, the effectiveness of these conditions is illustrated by two numerical examples.

On new stability results for generalized Cauchy functional equations on groups by using Brzdȩk’s fixed point theorem

In this work we present a new type of stability results for generalized Cauchy functional equation of the form $$f(ax \ast by) = af(x) \diamond bf(y),$$ where \({a, b \in \mathbb{N}}\) and \({f}\) is a mapping from a commutative semigroup (\({G_1, \ast}\)) to a commutative group (\({G_2, \diamond}\)). Using this form we generalize, extend and complement some earlier classical results concerning the stability of additive Cauchy functional equations. Our results are improvement and generalization of main results of Brzdȩk [Fixed Point Theory Appl. 2013 (2013), doi:10.1186/1687-1812-2013-285:285] and many results in literature. Some of the stability results for many types of functional equations are given here to illustrate the usability of the obtained results.

Exponential stability of uncertain differential equation

Uncertain differential equation is a type of differential equations involving uncertain processes. So far, the concepts of stability in measure and stability in mean have been proposed for uncertain differential equations. This paper proposes a new type of stability for uncertain differential equation, named exponential stability. Some examples are given to illustrate the concept, and the relationships between exponential stability, stability in measure and stability in mean are discussed. Besides, a sufficient and necessary condition for a linear uncertain differential equation being exponentially stable is derived.

α-stability and α-synchronization for fractional-order neural networks

In this paper, a class of fractional-order neural networks is investigated. First, @a-exponential stability is introduced as a new type of stability and some effective criteria are derived for such...

α-stability and α-synchronization for fractional-order neural networks

In this paper, a class of fractional-order neural networks is investigated. First, α-exponential stability is introduced as a new type of stability and some effective criteria are derived for such kind of stability of the addressed networks by handling a new fractional-order differential inequality. Based on the results, the existence and α-exponential stability of the equilibrium point are considered. Besides, the synchronization of fractional chaotic networks is also proposed. Finally, several examples with numerical simulations are given to show the effectiveness of the obtained results.

Global Lyapunov Analysis of Multistable Nonlinear Systems

A new type of stability is introduced and its equivalent Lyapunov characterization is presented. The problem of global stability for the compact set composed of all invariant solutions of a nonlinear system (several equilibriums, for instance) is studied. Such a problem statement allows us to analyze global stability properties for multistable systems. It is shown that several well-known multistable systems satisfy this new stability property.

Stability on a cone in terms of two measures for differential equations with ``maxima''

Stability in terms of two measures for nonlinear differential equations with ``maxima'' is studied. A special type of stability in terms of two measures is defined. The new type of stability generalizes some of the known in the literature. Sufficient conditions for the defined stability are obtained. Cone-valued continuous Lyapunov functions are applied. Method of Razumikhin as well as comparison method for scalar ordinary differential equations have been employed. The usefulness of the introduced definition and the obtained sufficient conditions is illustrated through an example.

On practical stability of perturbed differential systems

The notions of practical stability of systems of ordinary differential equations (ODE) was introduced. In this paper, we will extend practical stability notion to a new type of stability called practical ϕ 0-stability of perturbed systems of ordinary differential equations, and given Some criteria and results. Our technique depends on cone-vector Liapunov function method.

Total stability of perturbed systems of differential equations

The notion of Lipschitz stability for systems of ordinary differential equations (ODE) was introduced. In this paper, we will extend the total stability notion to a new type of stability called total Lipschitz stability. Some criteria and results are given. Our technique depends on Liapunov's direct method.

On total φ0-stability of nonlinear systems of differential equations

The notions of φ 0-stability of systems of ordinary differential equations (ODEs) were introduced. In this paper, we will extend the φ 0-stability notion to a new type of stability called total φ 0-stability, and give some criteria and results. Our technique depends on Liapunov's direct method.

On stability of perturbed impulsive differential systems

The notion of Lipschitz stability of impulsive systems of differential equations (DEs) was introduced. In this paper, we will extend the notion of eventual stability to impulsive systems of DEs and extend the notion of Lipschitz stability of impulsive systems of DEs to a new type of stability called eventual Lipschitz stability. Some criteria and results are given. Our technique depends on Liapunov's direct method and comparison principle.

On the stability of generalized state-space systems

In this paper, a duality property between regular and generalized state-space systems is presented. Using this property, the asymptotic, the BIBO, and the total stability for generalized state-space systems are studied. For asymptotic stability, new simple criteria are established. For BIBO and total stability, the criteria proposed are first in the field. A new type of stability is introduced, called the strong stability, for which simple criteria are established. >

On vector Lyapunov functions

It has been proved that the use of a vector Lyapunov function is more advantageous in certain situations rather than a scalar function. Moreover, each function needs to satisfy less rigid requirements. In this paper a new situation has been considered where vector Lyapunov functions play a further useful role. For this purpose, a new type of stability, namely, strict partial stability has been defined. The principal tool employed is the second method of Lyapunov and a comparision theorem of a more general type.

On a new type of stability

On a new type of stability