scholarly journals Absolute Stability and Master-Slave Synchronization of Systems with State-Dependent Nonlinearities

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Rong Li ◽  
Bo Liu ◽  
Chao Liu
Keyword(s):  
Absolute Stability ◽  
Schur Complement ◽  
Stability Conditions ◽  
Stability Criteria ◽  
Numerical Example ◽  
Kyp Lemma ◽  
State Dependent ◽  
The Stability ◽  
Stability Results

This paper is concerned with the problems of absolute stability and master-slave synchronization of systems with state-dependent nonlinearities. The Kalman-Yakubovich-Popov (KYP) lemma and the Schur complement formula are applied to get novel and less conservative stability conditions. A numerical example is presented to illustrate the efficiency of the stability criteria. Furthermore, a synchronization criterion is developed based on the proposed stability results.

scholarly journals On Some Sufficiency-Type Global Stability Results for Time-Varying Dynamic Systems with State-Dependent Parameterizations

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
M. De la Sen
Keyword(s):  
Global Stability ◽  
Dynamic Systems ◽  
Taylor Series Expansion ◽  
Time Varying ◽  
State Dependent ◽  
The Matrix ◽  
The Stability ◽  
Interval Type ◽  
Truncation Order ◽  
Stability Results

This paper formulates sufficiency-type global stability and asymptotic stability results for, in general, nonlinear time-varying dynamic systems with state-trajectory solution-dependent parameterizations. The stability proofs are based on obtaining sufficiency-type conditions which guarantee that either the norms of the solution trajectory or alternative interval-type integrals of the matrix of dynamics of the higher-order than linear terms do not grow faster than their available supremum on the preceding time intervals. Some extensions are also given based on the use of a truncated Taylor series expansion of chosen truncation order with multiargument integral remainder for the dynamics of the differential system.

scholarly journals Stability of Multi-Dimensional Birth-and-Death Processes with State-Dependent 0-Homogeneous Jumps

2014 ◽  
Vol 46 (01) ◽  
pp. 59-75 ◽  
Author(s):  
Matthieu Jonckheere ◽  
Seva Shneer
Keyword(s):  
Stochastic Systems ◽  
Direct Proof ◽  
Geometric Interpretation ◽  
Stability Conditions ◽  
Birth And Death Processes ◽  
Piecewise Constant ◽  
State Dependent ◽  
The Stability ◽  
Deterministic Dynamical System ◽  
Simple Geometric Interpretation

We study the conditions for positive recurrence and transience of multi-dimensional birth-and-death processes describing the evolution of a large class of stochastic systems, a typical example being the randomly varying number of flow-level transfers in a telecommunication wire-line or wireless network. First, using an associated deterministic dynamical system, we provide a generic method to construct a Lyapunov function when the drift is a smooth function on ℝN. This approach gives an elementary and direct proof of ergodicity. We also provide instability conditions. Our main contribution consists of showing how discontinuous drifts change the nature of the stability conditions and of providing generic sufficient stability conditions having a simple geometric interpretation. These conditions turn out to be necessary (outside a negligible set of the parameter space) for piecewise constant drifts in dimension two.

Stability Analysis for Descriptor Neutral Systems with Mixed Delays

2011 ◽  
Vol 228-229 ◽  
pp. 153-157
Author(s):  
Xiu Liu ◽  
Shou Ming Zhong ◽  
Xiu Yong Ding
Keyword(s):  
Descriptor System ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Neutral Systems ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Stability Results

Delay-dependent stability of descriptor neutral systems with mixed delays is investigated in this paper. Based on descriptor system approach, some new delay-dependent stability and robust stability criteria are established in terms of a operator and linear matrix inequalities(LMIs). Lyapunov-Krasovskii functional and Leibniz-Newton formula are applied to find the stability results.

scholarly journals Stability of Multi-Dimensional Birth-and-Death Processes with State-Dependent 0-Homogeneous Jumps

2014 ◽  
Vol 46 (1) ◽  
pp. 59-75 ◽  
Author(s):  
Matthieu Jonckheere ◽  
Seva Shneer
Keyword(s):  
Stochastic Systems ◽  
Direct Proof ◽  
Geometric Interpretation ◽  
Stability Conditions ◽  
Birth And Death Processes ◽  
Piecewise Constant ◽  
State Dependent ◽  
The Stability ◽  
Deterministic Dynamical System ◽  
Simple Geometric Interpretation

We study the conditions for positive recurrence and transience of multi-dimensional birth-and-death processes describing the evolution of a large class of stochastic systems, a typical example being the randomly varying number of flow-level transfers in a telecommunication wire-line or wireless network. First, using an associated deterministic dynamical system, we provide a generic method to construct a Lyapunov function when the drift is a smooth function on ℝN. This approach gives an elementary and direct proof of ergodicity. We also provide instability conditions. Our main contribution consists of showing how discontinuous drifts change the nature of the stability conditions and of providing generic sufficient stability conditions having a simple geometric interpretation. These conditions turn out to be necessary (outside a negligible set of the parameter space) for piecewise constant drifts in dimension two.

Numerical Stability Criteria for Localized Post-buckling Solutions in a Strut-on-Foundation Model

2004 ◽  
Vol 71 (3) ◽  
pp. 334-341 ◽  
Author(s):  
M. Khurram Wadee ◽  
Ciprian D. Coman ◽  
Andrew P. Bassom
Keyword(s):  
Total Potential Energy ◽  
Stability Criteria ◽  
Total Potential ◽  
All Solutions ◽  
Static Solutions ◽  
Foundation Model ◽  
Post Buckling ◽  
The Stability ◽  
Dead Loading ◽  
Stability Results

Some stability results are established for localized buckling solutions of a strut-on-foundation model which has an initially unstable post-buckling path followed by a restabilizing property. These results are in stark contrast with those for models with non-restabilizing behavior for which all solutions are unstable under dead-loading conditions. By approximating solutions with a nonperiodic set of functions, the stability of these static solutions can be assessed by examining the nature of the equilibrium using total potential energy considerations.

scholarly journals Stability of a Class of Hybrid Neutral Stochastic Differential Equations with Unbounded Delay

2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
Boliang Lu ◽  
Ruili Song
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Stochastic Differential Equations ◽  
Lyapunov Functions ◽  
Stability Criteria ◽  
Bounded Delay ◽  
Unbounded Delay ◽  
The Stability ◽  
Generalized Itô Formula ◽  
Stability Results

This paper studies the stability of hybrid neutral stochastic differential equations with unbounded delay. Some novel exponential stability criteria and boundedness conditions are established based on the generalized Itô formula and Lyapunov functions. The factor e-εδ(t) is used to overcome the difficulties caused by the unbounded delay δ(t) effectively. In particular, our results generalize and improve some previous stability results from bounded delay to unbounded delay conditions. Finally, an example is presented to demonstrate the effectiveness of the proposed results.

Stability and Regularization of Difference Schemes in Banach and Hilbert Spaces

2013 ◽  
Vol 13 (2) ◽  
pp. 139-160
Author(s):  
Ivan P. Gavrilyuk ◽  
Volodymyr L. Makarov
Keyword(s):  
Banach Space ◽  
Adjoint Operator ◽  
Sufficient Conditions ◽  
Iteration Scheme ◽  
Difference Schemes ◽  
Stability Conditions ◽  
Initial Operator ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Stability Results

Abstract. The necessary and sufficient conditions for stability of abstract difference schemes in Hilbert and Banach spaces are formulated. Contrary to known stability results we give stability conditions for schemes with non-self-adjoint operator coefficients in a Hilbert space and with strongly positive operator coefficients in a Banach space. It is shown that the parameters of the sectorial spectral domain play the crucial role. As an application we consider the Richardson iteration scheme for an operator equation in a Banach space, in particulary the Richardson iteration with precondition for a finite element scheme for a non-selfadjoint operator. The theoretical results are also the basis when using the regularization principle to construct stable difference schemes. For this aim we start from some simple scheme (even unstable) and derive stable schemes by perturbing the initial operator coefficients and by taking into account the stability conditions. Our approach is also valid for schemes with unbounded operator coefficients.

Epitaxial Growth in Dislocation-Free Strained Alloy Films

2002 ◽  
Vol 715 ◽  
Author(s):  
Zhi-Feng Huang ◽  
Rashmi C. Desai
Keyword(s):  
Deposition Rate ◽  
Elastic Moduli ◽  
Composition Dependence ◽  
Critical Thickness ◽  
Lattice Misfit ◽  
Misfit Strain ◽  
Joint Stability ◽  
Alloy Films ◽  
The Stability ◽  
Stability Results

AbstractThe morphological and compositional instabilities in the heteroepitaxial strained alloy films have attracted intense interest from both experimentalists and theorists. To understand the mechanisms and properties for the generation of instabilities, we have developed a nonequilibrium, continuum model for the dislocation-free and coherent film systems. The early evolution processes of surface pro.les for both growing and postdeposition (non-growing) thin alloy films are studied through a linear stability analysis. We consider the coupling between top surface of the film and the underlying bulk, as well as the combination and interplay of different elastic effects. These e.ects are caused by filmsubstrate lattice misfit, composition dependence of film lattice constant (compositional stress), and composition dependence of both Young's and shear elastic moduli. The interplay of these factors as well as the growth temperature and deposition rate leads to rich and complicated stability results. For both the growing.lm and non-growing alloy free surface, we determine the stability conditions and diagrams for the system. These show the joint stability or instability for film morphology and compositional pro.les, as well as the asymmetry between tensile and compressive layers. The kinetic critical thickness for the onset of instability during.lm growth is also calculated, and its scaling behavior with respect to misfit strain and deposition rate determined. Our results have implications for real alloy growth systems such as SiGe and InGaAs, which agree with qualitative trends seen in recent experimental observations.

scholarly journals Causality and stability conditions of a conformal charged fluid

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Farid Taghinavaz
Keyword(s):  
Chemical Potential ◽  
Second Law Of Thermodynamics ◽  
Dense Medium ◽  
Wave Number ◽  
Second Law ◽  
Stability Conditions ◽  
Charged Fluid ◽  
Large Wave ◽  
The Stability ◽  
Large Wave Number

Abstract In this paper, I study the conditions imposed on a normal charged fluid so that the causality and stability criteria hold for this fluid. I adopt the newly developed General Frame (GF) notion in the relativistic hydrodynamics framework which states that hydrodynamic frames have to be fixed after applying the stability and causality conditions. To do this, I take a charged conformal matter in the flat and 3 + 1 dimension to analyze better these conditions. The causality condition is applied by looking to the asymptotic velocity of sound hydro modes at the large wave number limit and stability conditions are imposed by looking to the imaginary parts of hydro modes as well as the Routh-Hurwitz criteria. By fixing some of the transports, the suitable spaces for other ones are derived. I observe that in a dense medium having a finite U(1) charge with chemical potential μ0, negative values for transports appear and the second law of thermodynamics has not ruled out the existence of such values. Sign of scalar transports are not limited by any constraints and just a combination of vector transports is limited by the second law of thermodynamic. Also numerically it is proved that the most favorable region for transports $$ {\tilde{\upgamma}}_{1,2}, $$ γ ˜ 1 , 2 , coefficients of the dissipative terms of the current, is of negative values.

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