http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
Yuangong Sun,Zhi Liu 한국전산응용수학회 2013 Journal of applied mathematics & informatics Vol.31 No.1
In this paper, we study the oscillation problem of the followinghigher-order neutral differential equation with positive and negativecoefficients and mixed argumentsz(n)(t)+q1(t)|x(t-σ1)jα-1x(t-σ1)+q2(t)|x(t-σ2)|β-1x(t-σ2) = e(t), where t≥ t0, z(t) = x(t) - p(t)x(t - τ) with p(t) > 0, β > 1 > α > 0, τ, σ1 and σ2 are real numbers. Without imposing any restriction on τ, we establish several oscillation criteria for the above equation in two cases:(i) q1(t) ≤ 0, q2(t) > 0, σ1 ≥ 0 and σ2 ≤τ; (ii) q1(t) ≥ 0, q2(t) < 0, σ1 ≥ τ and σ2 ≤ 0. As an interesting application, our results can alsobe applied to the following higher-order differential equation with positiveand negative coefficients and mixed argumentsx(n)(t)+q1(t)jx(t-σ1)|α-1x(t-σ1)+q2(t)|x(t-σ2)|β-1x(t-σ2) = e(t). Two numerical examples are also given to illustrate the main results.
Sun, Yuangong,Liu, Zhi The Korean Society for Computational and Applied M 2013 Journal of applied mathematics & informatics Vol.31 No.1
In this paper, we study the oscillation problem of the following higher-order neutral differential equation with positive and negative coefficients and mixed arguments $$z^{(n)}(t)+q_1(t)|x(t-{\sigma}_1)|^{\alpha-1}x(t-{\sigma}_1)+q_2(t)|x(t-{\sigma}_2)|^{\beta-1}x(t-{\sigma}_2)=e(t)$$, where $t{\geq}t_0$, $z(t)=x(t)-p(t)x(t-{\tau})$ with $p(t)$ > 0, ${\beta}>1>{\alpha}>0$, ${\tau}$, ${\sigma}_1$ and ${\sigma}_2$ are real numbers. Without imposing any restriction on ${\tau}$, we establish several oscillation criteria for the above equation in two cases: (i) $q_1(t){\leq}0$, $q_2(t)>0$, ${\sigma}_1{\geq}0$ and ${\sigma}_2{\leq}{\tau}$; (ii) $q_1(t){\geq}0$, $q_2(t)<0$, ${\sigma}_1{\geq}{\tau}$ and ${\sigma}_2{\leq}0$. As an interesting application, our results can also be applied to the following higher-order differential equation with positive and negative coefficients and mixed arguments $$x^{(n)}(t)+q_1(t)|x(t-{\sigma}_1)|^{\alpha-1}x(t-{\sigma}_1)+q_2(t)|x(t-{\sigma}_2)|^{\beta-1}x(t-{\sigma}_2)=e(t)$$. Two numerical examples are also given to illustrate the main results.
Stability of generalized homogeneous cooperative systems
Yang Xu,Yuangong Sun 제어로봇시스템학회 2022 제어로봇시스템학회 국제학술대회 논문집 Vol.2022 No.11
In this paper, we study the asymptotic stability of nonlinear cooperative system by introducing a class of generalized homogeneous vector fields. With the help of the analytical techniques developed in homogeneous cooperative systems, we establish sufficient conditions for the global asymptotic stability of generalized homogeneous cooperative systems with time delays. When the involved system degenerates into a homogeneous cooperative system, sufficient and necessary conditions for the stability of the system are proposed. A simulation example is given to show the practicability of the conclusion.
Stability of Switching Linear Uncertain Systems via switching time-varying Lyapunov functions
Huimin Zheng,Yuangong Sun 제어로봇시스템학회 2022 제어로봇시스템학회 국제학술대회 논문집 Vol.2022 No.11
In this article, the global asymptotic stability of switching linear uncertain systems with all subsystems unstable is investigated. By introducing a switching time-varying Lyapunov function, new criteria are proposed to ensure that the involved system is globally uniformly asymptotically stable (GUAS) under the mode-dependent range dwell time (MDRDT) frame by using the stability of switching behavior to counteract the state divergence generated by unstable subsystems and using linear matrix inequality to deal with uncertainty. Finally, a numerical example is worked out to illustrate the feasibility of the method.
Finite-time stability of uncertain singular systems based on time-varying Lyapunov function
Mei Meng,Yuangong Sun 제어로봇시스템학회 2022 제어로봇시스템학회 국제학술대회 논문집 Vol.2022 No.11
This paper addresses the finite-time stability (FTS) and H<SUB>∞</SUB> FTS of uncertain singular systems. At first, a class of time-dependent Lyapunov functions are constructed by using the convex combination method, and a class of zero terms with a convex combination of freely weighted matrices are introduced to get the desired results. Then the new explicit sufficient conditions for FTS and H<SUB>∞</SUB> FTS of the uncertain singular systems are given by using LMI. These conditions guarantee the regularity and impulse-free of the uncertain singular systems. Finally, by using the LMI toolbox in the MATLAB, two numerical examples are given to verify the validity of the developed results.
Na Jiang,Yuangong Sun 제어로봇시스템학회 2022 제어로봇시스템학회 국제학술대회 논문집 Vol.2022 No.11
This article investigates some new exponential stability criteria of discrete-time switched systems with both disturbance and impulse. By introducing a novel multiple switched time-varying matrix function, sufficient conditions are presented to ensure the discrete-time switched system to be exponentially stable and achieve H<SUB>∞</SUB> performance under the mode-dependent interval dwell-time switching. Eventually, two numerical examples with unstable subsystems are presented which verify the validity of our conclusions.
Chao Wang,Yuangong Sun 제어로봇시스템학회 2022 제어로봇시스템학회 국제학술대회 논문집 Vol.2022 No.11
This article deals with the dwell time stability problem of discrete-time positive linear switching delay systems with interval uncertainties. A new time-varying Lyapunov function is constructed by the method of expanding the dimension. Both the mode-dependent range dwell time and the mode-dependent minimum dwell time are taken into consideration. New stability criteria of the system are presented under two types of switching signals. All the results are obtain by using linear inequalities that can be verified based on the linear programming (LP). In the end, some examples are proposed to illustrate the correctness and validity of our results.
Qian Ma,Yuangong Sun 제어·로봇·시스템학회 2022 International Journal of Control, Automation, and Vol.20 No.4
In this paper, the finite time stability and H∞ finite-time stability of singular linear systems are considered. By constructing a class of time-dependent Lyapunov functions and introducing a zero term with free weighting matrices, we first establish a new explicit criterion in the form of LMIs for finite-time stability of the system. Then, an H∞ finite-time stability criterion for the system is obtained. The given results are easily verifiable and less conservative compared with some existing ones in the literature. Finally, four numerical examples are given to demonstrate the effectiveness of the proposed method.
Stabilization of Switched Systems with Uncontrollable Subsystems
Yanli Zhu,Yuangong Sun 한국전산응용수학회 2013 Journal of applied mathematics & informatics Vol.31 No.5
In this paper, we study the stabilization problem of switched systems with both controllable and uncontrollable subsystems. By using an average dwell time approach, we first establish a sufficient condition such that the switched system is exponentially stabilizable under appropriate switching signals. We also extend this result to the switched system with nonlinear impulse effects and disturbances. Numerical examples are given to illustrate the theoretical results.