scholarly journals Stability criteria for nonlinear Volterra integro-dynamic matrix Sylvester systems on measure chains

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sreenivasulu Ayyalappagari ◽  
Venkata Appa Rao Bhogapurapu
Keyword(s):  
Asymptotic Stability ◽  
Exponential Stability ◽  
Dynamic System ◽  
Time Scale ◽  
Sufficient Conditions ◽  
Strong Stability ◽  
Discrete Models ◽  
Stability Criteria ◽  
Dynamic Matrix ◽  
The Matrix

AbstractIn this paper, we establish sufficient conditions for various stability aspects of a nonlinear Volterra integro-dynamic matrix Sylvester system on time scales. We convert the nonlinear Volterra integro-dynamic matrix Sylvester system on time scale to an equivalent nonlinear Volterra integro-dynamic system on time scale using vectorization operator. Sufficient conditions are obtained to this system for stability, asymptotic stability, exponential stability, and strong stability. The obtained results include various stability aspects of the matrix Sylvester systems in continuous and discrete models.

scholarly journals Asymptotic Stability of Caputo Type Fractional Neutral Dynamical Systems with Multiple Discrete Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Hai Zhang ◽  
Daiyong Wu ◽  
Jinde Cao
Keyword(s):  
Asymptotic Stability ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Algebraic Approach ◽  
Stability Criteria ◽  
Differential Systems ◽  
Discrete Delays ◽  
Transcendental Equations ◽  
The Stability ◽  
Theoretical Results

We discuss the delay-independent asymptotic stability of Caputo type fractional-order neutral differential systems with multiple discrete delays. Based on the algebraic approach and matrix theory, the sufficient conditions are derived to ensure the asymptotic stability for all time-delay parameters. By applying the stability criteria, one can avoid solving the roots of transcendental equations. The results obtained are computationally flexible and convenient. Moreover, an example is provided to illustrate the effectiveness and applicability of the proposed theoretical results.

scholarly journals Stability and stabilization of linear positive systems on time scales

Positivity ◽  
2020 ◽  
Vol 24 (5) ◽  
pp. 1361-1372
Author(s):  
Zbigniew Bartosiewicz
Keyword(s):  
Control System ◽  
Linear System ◽  
Time Scale ◽  
Sufficient Conditions ◽  
Positive Control ◽  
Positive Systems ◽  
The Matrix ◽  
Exponentially Stable ◽  
Stability And Stabilization ◽  
Necessary And Sufficient

Abstract It is shown that a positive linear system on a time scale with a bounded graininess is uniformly exponentially stable if and only if the characteristic polynomial of the matrix defining the system has all its coefficients positive. Then this fact is used to find necessary and sufficient conditions of positive stabilizability of a positive control system on a time scale.

scholarly journals Oscillation for a Nonlinear Dynamic System with a Forced Term on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Xinli Zhang ◽  
Shanliang Zhu
Keyword(s):  
Dynamic System ◽  
Time Scale ◽  
Nonlinear Dynamic ◽  
Sufficient Conditions ◽  
Nonlinear Dynamic System ◽  
Two Dimensional ◽  
Differential Systems ◽  
Difference Systems ◽  
All Solutions ◽  
Forced Term

We consider a class of two-dimensional nonlinear dynamic system with a forced term on a time scale𝕋and obtain sufficient conditions for all solutions of the system to be oscillatory. Our results not only unify the oscillation of two-dimensional differential systems and difference systems but also improve the oscillation results that have been established by Saker, 2005, since our results are not restricted to the case whereb(t)≠0for allt∈𝕋andg(u)=u. Some examples are given to illustrate the results.

scholarly journals On Stability Analysis for Generalized Neural Networks with Time-Varying Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
M. J. Park ◽  
O. M. Kwon ◽  
E. J. Cha
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Asymptotic Stability ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Numerical Examples ◽  
Generalized Neural Networks

This paper deals with the problem of stability analysis for generalized neural networks with time-varying delays. With a suitable Lyapunov-Krasovskii functional (LKF) and Wirtinger-based integral inequality, sufficient conditions for guaranteeing the asymptotic stability of the concerned networks are derived in terms of linear matrix inequalities (LMIs). By applying the proposed methods to two numerical examples which have been utilized in many works for checking the conservatism of stability criteria, it is shown that the obtained results are significantly improved comparing with the previous ones published in other literature.

Exponential Stability of Stochastic Age-Dependent Population with Diffusion

2011 ◽  
Vol 282-283 ◽  
pp. 231-235
Author(s):  
Hui Li Han ◽  
Qi Min Zhang
Keyword(s):  
Hilbert Space ◽  
Exponential Stability ◽  
Dynamic System ◽  
Population Dynamic ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Strong Solutions ◽  
Exponential Martingale ◽  
Age Dependent ◽  
The Stability

In this paper, a class of stochastic age-dependent population dynamic system with diffusion is introduced. Exponential stability of paths of a strong solution for stochastic age-dependent population dynamic system in Hilbert space is established. The analyses use exponential martingale formula, Lyapunov functional and some special inequalities for our stability purposes. Various sufficient conditions are obtained to ensure the stability of the strong solutions. In particular, by means of our results we loosen the condition of stability.

Exponential Stability for Grey Linear Systems with Time-Varying Delay

2013 ◽  
Vol 760-762 ◽  
pp. 2258-2262
Author(s):  
Ji Chao Wang ◽  
Li Jun Song ◽  
Wei Liu ◽  
Jin Fang Han
Keyword(s):  
Exponential Stability ◽  
Linear Systems ◽  
Stability Problem ◽  
Measure Theory ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Matrix Measure ◽  
Time Varying Delay ◽  
The Matrix ◽  
Varying Delay

In this paper, the exponential stability problem of grey linear systems with time-varying delay is investigated. By using the matrix measure theory and differential inequality approach, some practical sufficient conditions for guaranteeing the exponential stability of the grey linear systems with time-varying delay are presented. The grey-matrix measure and norm are also introduced.

scholarly journals Hybrid nonnegative and computational dynamical systems

2002 ◽  
Vol 8 (6) ◽  
pp. 493-515 ◽  
Author(s):  
Wassim M. Haddad ◽  
Vijaysekhar Chellaboina ◽  
Sergey G. Nersesov
Keyword(s):  
Dynamical Systems ◽  
Asymptotic Stability ◽  
Conservation Laws ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Hybrid Structures ◽  
Stability Criteria ◽  
General Stability ◽  
Feedback Interconnections ◽  
Flow Laws

Nonnegative and Compartmental dynamical systems are governed by conservation laws and are comprised of homogeneous compartments which exchange variable nonnegative quantities of material via intercompartmental flow laws. These systems typically possess hierarchical (and possibly hybrid) structures and are remarkably effective in capturing the phenomenological features of many biological and physiological dynamical systems. In this paper we develop several results on stability and dissipativity of hybrid nonnegative and Compartmental dynamical systems. Specifically, usinglinearLyapunov functions we develop sufficient conditions for Lyapunov and asymptotic stability for hybrid nonnegative dynamical systems. In addition, usinglinearandnonlinearstorage functions withlinearhybrid supply rates we developnewnotions of dissipativity theory for hybrid nonnegative dynamical systems. Finally, these results are used to develop general stability criteria for feedback interconnections of hybrid nonnegative dynamical systems.

Study of Complex Networked Control System Exponential Stability

2014 ◽  
Vol 926-930 ◽  
pp. 2106-2109
Author(s):  
Yue Pan
Keyword(s):  
Control System ◽  
Exponential Stability ◽  
Dynamic System ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Integrated Model ◽  
Networked Control System ◽  
Data Loss ◽  
Closed Loop System ◽  
Necessary And Sufficient

An integrated model considering all complex factors was provided. Combined with data Loss Tolerance and build an asynchronous dynamic system consisting observer and controller in the closed-loop system. The necessary and sufficient conditions to make the system index stable were analyzed.

Exponential Stability Criteria for Neutral System with Mixed Time-Varying Delays and Nonlinear Perturbations

2013 ◽  
Vol 787 ◽  
pp. 891-895 ◽  
Author(s):  
Shao Ying Wang ◽  
Fang Qiu ◽  
Xue Gang Tian
Keyword(s):  
Exponential Stability ◽  
Sufficient Conditions ◽  
Neutral System ◽  
Time Varying ◽  
Nonlinear Perturbations ◽  
Stability Criteria ◽  
Neutral Systems ◽  
Numerical Examples

This paper focuses on the issue of robustly exponential stability for uncertain neutral systems with mixed time-varying delays and nonlinear perturbations. Some new sufficient conditions dependent on the delays are derived in terms of Lyapunov-Krasovskii functionals combined with free-weighting matrices. Two numerical examples are given to show the effectiveness of the proposed method.

Simple algebraic necessary and sufficient conditions for Lyapunov stability of a Chen system and their applications

2017 ◽  
Vol 40 (7) ◽  
pp. 2200-2210 ◽  
Author(s):  
Guopeng Zhou ◽  
Xiaoxin Liao ◽  
Bingji Xu ◽  
Pei Yu ◽  
Guanrong Chen
Keyword(s):  
Asymptotic Stability ◽  
Exponential Stability ◽  
Lyapunov Stability ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Linear Feedback ◽  
Chen System ◽  
Local Asymptotic Stability ◽  
Positive Elements ◽  
Necessary And Sufficient

In this paper, we study the Lyapunov stability problem of a Chen chaotic system. Because of the positive elements of the main diagonal of a linearized Chen system, compared to the coefficient of a linearized Lorenz system which are all negative, it is more difficult to deal with the stability analysis. Since it has the properties of invariance and symmetry, different Lyapunov functions in different regions are constructed to solve stability problems with geometric and algebraic methods. Then, simple algebraic necessary and sufficient conditions of global exponential stability, global asymptotic stability and global instability of equilibrium [Formula: see text] are proposed. We obtain the relevant expression of corresponding parameters for local exponential stability, local asymptotic stability and local instability of equilibria [Formula: see text]. Furthermore, the smallest conservative linear feedback controllers are used to globally exponentially stabilize equilibria.

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