The controlled objects are uncertain stable,but the optimal control systems which are constituted by the controlled objects under certain conditions are certain stable. This paper analyses stability of optimal control...The controlled objects are uncertain stable,but the optimal control systems which are constituted by the controlled objects under certain conditions are certain stable. This paper analyses stability of optimal control systems which have quadric performance index via Liapunov method.展开更多
Liapunov's 2nd method is applied to analyse the Stability of a ciamped poleorthotropic round plate acted by a radial axisymmetrical impact load on its periphery. The analysis is carried cut under the assumptions o...Liapunov's 2nd method is applied to analyse the Stability of a ciamped poleorthotropic round plate acted by a radial axisymmetrical impact load on its periphery. The analysis is carried cut under the assumptions of small deflection and elasticity The impact load is supposed to have a step impulsive form. A sufficient stability condition is given.展开更多
In this paper, the stability with respect to partial variables for the Birkhoff system is studied. By transplanting the results of the partial stability for general systems to the Birkhoff system and constructing a su...In this paper, the stability with respect to partial variables for the Birkhoff system is studied. By transplanting the results of the partial stability for general systems to the Birkhoff system and constructing a suitable Liapunov function, the partial stability of the system can be achieved. Finally, two examples are given to illustrate the application of the results.展开更多
By the use of the Liapunov functional approach, a new result is obtained to ascertain the asymptotic stability of zero solution of a certain fourth-order non-linear differential equation with delay. The established re...By the use of the Liapunov functional approach, a new result is obtained to ascertain the asymptotic stability of zero solution of a certain fourth-order non-linear differential equation with delay. The established result is less restrictive than those reported in the literature.展开更多
In this paper, global asymptotic stability for cellular neural networks with time delay is discussed using a novel Liapunov function. Some novel sufficient conditions for global asymptotic stability are obtained. Thos...In this paper, global asymptotic stability for cellular neural networks with time delay is discussed using a novel Liapunov function. Some novel sufficient conditions for global asymptotic stability are obtained. Those results are simple and practical than those given by P. P. Civalleri, et al., and have a leading importance to design cellular neural networks with time delay.展开更多
By constructing Liapunov functions and building a new inequality, we obtain two kinds of sufficient conditions for the existence and global exponential stability of almost periodic solution for a Hopfield-type neural ...By constructing Liapunov functions and building a new inequality, we obtain two kinds of sufficient conditions for the existence and global exponential stability of almost periodic solution for a Hopfield-type neural networks subject to almost periodic external stimuli. Irt this paper, we assume that the network parameters vary almost periodically with time and we incorporate variable delays in the processing part of the network architectures.展开更多
The coal mine roof rating(CMRR) was developed to bridge the gap between geological variation in underground coal mines and engineering design. The CMRR accounts for the compressive strength of the immediate roof, the ...The coal mine roof rating(CMRR) was developed to bridge the gap between geological variation in underground coal mines and engineering design. The CMRR accounts for the compressive strength of the immediate roof, the shear strength and intensity of any discontinuities present, and the moisture sensitivity of the immediate roof. The CMRR has been widely used and validated in Eastern US coal mines, but it has seen limited application in the Western US. This study focuses on roof behavior at a Western coal mine(Mine A). Mine A shows significant lateral geological variation, along with localized faulting and a laterally extensive sandstone channel network. The CMRR is not used to predict roof instability at the mine. It is, therefore, hypothesized that there are other factors that are correlated with roof instability in underground coal mines that could potentially also be considered in conjunction with the CMRR.This hypothesis was tested by collecting 30 CMRR measurements at Mine A. At each measurement location, a binary record of the roof condition(stable or unstable) was made, and other parameters such as depth of cover, presence of faulting, and sandstone channels were also recorded. ANOVA tests showed that the CMRR values and the roof conditions were not strongly correlated, indicating that the CMRR input criteria are not fully predictive of roof stability at this mine. The CMRR values showed statistically significant correlations(p less than 0.05) with faulting as well as with location at an intersection. For areas that had previously experienced roof fall but were currently stable, faulting was correlated with roof condition(p less than 0.05) only when the condition was classified as unstable.展开更多
The stability of the motion control system is one of the decisive factors of the control quality for Autonomous Underwater Vehicle(AUV).The divergence of control,which the unstable system may be brought about,is fat...The stability of the motion control system is one of the decisive factors of the control quality for Autonomous Underwater Vehicle(AUV).The divergence of control,which the unstable system may be brought about,is fatal to the operation of AUV.The stability analysis of the PD and S-surface speed controllers based on the Lyapunov's direct method is proposed in this paper.After decoupling the six degree-of-freedom(DOF)motions of the AUV,the axial dynamic behavior is discussed and the condition is deduced,in which the parameters selection within stability domain can guarantee the system asymptotically stable.The experimental results in a tank and on the sea have successfully verified the algorithm reliability,which can be served as a good reference for analyzing other AUV nonlinear control systems.展开更多
Helical equilibrium of a thin elastic rod has practical backgrounds, such as DNA, fiber, sub-ocean cable, and oil-well drill string. Kirchhoff's kinetic analogy is an effective approach to the stability analysis of e...Helical equilibrium of a thin elastic rod has practical backgrounds, such as DNA, fiber, sub-ocean cable, and oil-well drill string. Kirchhoff's kinetic analogy is an effective approach to the stability analysis of equilibrium of a thin elastic rod. The main hypotheses of Kirchhoff's theory without the extension of the centerline and the shear deformation of the cross section are not adoptable to real soft materials of biological fibers. In this paper, the dynamic equations of a rod with a circular cross section are established on the basis of the exact Cosserat model by considering the tension and the shear deformations. Euler's angles are applied as the attitude representation of the cross section. The deviation of the normal axis of the cross section from the tangent of the centerline is considered as the result of the shear deformation. Lyapunov's stability of the helical equilibrium is discussed in static category. Euler's critical values of axial force and torque are obtained. Lyapunov's and Euler's stability conditions in the space domain are the necessary conditions of Lyapunov's stability of the helical rod in the time domain.展开更多
In this paper, we investigate the stability of a class of impulsive functional differential equations by using Lyapunov functional and Jensen's inequality. Some new stability theorems are obtained. Examples are given...In this paper, we investigate the stability of a class of impulsive functional differential equations by using Lyapunov functional and Jensen's inequality. Some new stability theorems are obtained. Examples are given to demonstrate the advantage of the obtained results.展开更多
Sufficient condition for stochastic unifrom stability of a neutral stochastic functional differential equation is given, especially, new techniques are developed to cope with the neutral delay case, we obtained the su...Sufficient condition for stochastic unifrom stability of a neutral stochastic functional differential equation is given, especially, new techniques are developed to cope with the neutral delay case, we obtained the sufficient condition for asymptotic stability of neutral stochastic differential delay equations. Due to the new techniques developed in this paper, the results obtained arc very general and useful. The theory developed here gives a unified treatment for various asymptotic estimates e.g. exponential and polynomial bounds.展开更多
In this paper, we have discussed the linear stabil- ity analysis of the electrified surface separating two coaxial Oldroyd-B fluid layers confined between two impermeable rigid cylinders in the presence of both interf...In this paper, we have discussed the linear stabil- ity analysis of the electrified surface separating two coaxial Oldroyd-B fluid layers confined between two impermeable rigid cylinders in the presence of both interfacial insoluble surfactant and surface charge through porous media. The case of long waves interfacial stability has been studied. The dispersion relation is solved numerically and hence the ef- fects of various parameters are illustrated graphically. Our results reveal that the influence of the physicochemical pa- rameterβ is to shrink the instability region of the surface and reduce the growth rate of the unstable normal modes. Such important effects of the surfactant on the shape of in- terfacial structures are more sensitive to the variation of the βcorresponding to non-Newtonian fluids-model compared with the Newtonian fluids model. In the case of long wave limit, it is demonstrated that increasing r, has a dual role in- fluence (de-stabilizing effects) depending on the viscosity of the core fluid. It has a destabilizing effect at the large values of the core fluid viscosity coefficient, while this role is ex- changed to a regularly stabilizing influence at small values of such coefficient.展开更多
In this paper,an eco-epidemiological model with Beddington-DeAngelis functional response and a time delay representing the gestation period of the predator is studied.By means of Lyapunov functionals and Laselle’s i...In this paper,an eco-epidemiological model with Beddington-DeAngelis functional response and a time delay representing the gestation period of the predator is studied.By means of Lyapunov functionals and Laselle’s invariance principle,sufficient conditions are obtained for the global stability of the interior equilibrium and the disease-free equilibrium of the system,respectively.展开更多
To alleviate the conservativeness of the stability criterion for Takagi-Sugeno(T-S)fuzzy time-delay systems,a new delay-dependent stability criterion was proposed by introducing a new augmented Lyapunov function with ...To alleviate the conservativeness of the stability criterion for Takagi-Sugeno(T-S)fuzzy time-delay systems,a new delay-dependent stability criterion was proposed by introducing a new augmented Lyapunov function with an additional triple-integral term,which was firstly used to derive the stability criterion for T-S fuzzy time-delay systems.By the same approach,the robust stability issue for fuzzy time-delay systems with uncertain parameters was also considered.On the other hand,in order to enhance the design flexibility,a new design approach for uncertain fuzzy time-delay systems under imperfect premise matching was also proposed,which allows the fuzzy controller to employ different membership functions from the fuzzy time-delay model.By the numerical examples,the proposed stability conditions are less conservative in the sense of getting larger allowable time-delay and obtaining smaller feedback control gains.For instance,when the allowable time-delay increases from 7.3s to 12s for an uncertain T-S fuzzy control system with time-delay,the norm of the feedback gains decreases from(34.299 2,38.560 3)to(10.073 3,11.349 0),respectively.Meanwhile,the effectiveness of the proposed design method was illustrated by the last example with the robustly stable curves of system state under the initial condition ofx(0)=[3-1].展开更多
The stability of second-order differential equations is studied by using their integrals. A system of second-order differential equations can be considered as a mechanical system with holonomic constraints. A conserve...The stability of second-order differential equations is studied by using their integrals. A system of second-order differential equations can be considered as a mechanical system with holonomic constraints. A conserved quantity of the mechanical system or a part of the system is obtained by using the Noether theory. It is possible that the conserved quantity becomes a Liapunov function and the stability of the system is proved by the Liapunov theorem.展开更多
The cellular neural networks with delay (DCNN’s) are investigated, and some new sufficient conditions on asymptotical stability of DCNN’s are derived by constructing the Liapunov functional and utilizing M ? matrixa...The cellular neural networks with delay (DCNN’s) are investigated, and some new sufficient conditions on asymptotical stability of DCNN’s are derived by constructing the Liapunov functional and utilizing M ? matrixand theω?limit set. It is shown that the new conditions are not related to the delayed parameter.展开更多
In this paper, we present a new sufficient condition for absolute stability of Lure system with two additive time-varying delay components. This criterion is expressed as a set of linear matrix inequalities (LMIs), ...In this paper, we present a new sufficient condition for absolute stability of Lure system with two additive time-varying delay components. This criterion is expressed as a set of linear matrix inequalities (LMIs), which can be readily tested by using standard numerical software. We use this new criterion to stabilize a class of nonlinear time-delay systems. Some numerical examples are given to illustrate the applicability of the results using standard numerical software.展开更多
In this paper,the author investigates uuiform stability,asymptotic stability,and uniform asymptotic stability forthe zero solution of neutral functional differentialequations.Some well-known results are improved.
By using the variational Liapunov method, stability properties in terms of two measures for delay differential equations are discussed. In the case that the unperturbed systems are ordinary differential systems, emplo...By using the variational Liapunov method, stability properties in terms of two measures for delay differential equations are discussed. In the case that the unperturbed systems are ordinary differential systems, employing auxiliary measure h*(t, x), criteria on nonuniform and uniform stability in terms of two measures for delay differential equations are established.展开更多
文摘The controlled objects are uncertain stable,but the optimal control systems which are constituted by the controlled objects under certain conditions are certain stable. This paper analyses stability of optimal control systems which have quadric performance index via Liapunov method.
文摘Liapunov's 2nd method is applied to analyse the Stability of a ciamped poleorthotropic round plate acted by a radial axisymmetrical impact load on its periphery. The analysis is carried cut under the assumptions of small deflection and elasticity The impact load is supposed to have a step impulsive form. A sufficient stability condition is given.
基金Project supported by the National Natural Science Foundation of China (Grant No 10572021) and the Doctoral Program Foun dation of Institution of Higher Education, China (Grant No 20040007022).
文摘In this paper, the stability with respect to partial variables for the Birkhoff system is studied. By transplanting the results of the partial stability for general systems to the Birkhoff system and constructing a suitable Liapunov function, the partial stability of the system can be achieved. Finally, two examples are given to illustrate the application of the results.
文摘By the use of the Liapunov functional approach, a new result is obtained to ascertain the asymptotic stability of zero solution of a certain fourth-order non-linear differential equation with delay. The established result is less restrictive than those reported in the literature.
文摘In this paper, global asymptotic stability for cellular neural networks with time delay is discussed using a novel Liapunov function. Some novel sufficient conditions for global asymptotic stability are obtained. Those results are simple and practical than those given by P. P. Civalleri, et al., and have a leading importance to design cellular neural networks with time delay.
基金The Soft Project (B30145) of Science and Technology of Hunan Province.
文摘By constructing Liapunov functions and building a new inequality, we obtain two kinds of sufficient conditions for the existence and global exponential stability of almost periodic solution for a Hopfield-type neural networks subject to almost periodic external stimuli. Irt this paper, we assume that the network parameters vary almost periodically with time and we incorporate variable delays in the processing part of the network architectures.
基金supported by a NIOSH Capacity Building grant (No. 200-2016-90154) to Drs. G. Walton and E. Holley and collaborators at the Colorado School of Mines
文摘The coal mine roof rating(CMRR) was developed to bridge the gap between geological variation in underground coal mines and engineering design. The CMRR accounts for the compressive strength of the immediate roof, the shear strength and intensity of any discontinuities present, and the moisture sensitivity of the immediate roof. The CMRR has been widely used and validated in Eastern US coal mines, but it has seen limited application in the Western US. This study focuses on roof behavior at a Western coal mine(Mine A). Mine A shows significant lateral geological variation, along with localized faulting and a laterally extensive sandstone channel network. The CMRR is not used to predict roof instability at the mine. It is, therefore, hypothesized that there are other factors that are correlated with roof instability in underground coal mines that could potentially also be considered in conjunction with the CMRR.This hypothesis was tested by collecting 30 CMRR measurements at Mine A. At each measurement location, a binary record of the roof condition(stable or unstable) was made, and other parameters such as depth of cover, presence of faulting, and sandstone channels were also recorded. ANOVA tests showed that the CMRR values and the roof conditions were not strongly correlated, indicating that the CMRR input criteria are not fully predictive of roof stability at this mine. The CMRR values showed statistically significant correlations(p less than 0.05) with faulting as well as with location at an intersection. For areas that had previously experienced roof fall but were currently stable, faulting was correlated with roof condition(p less than 0.05) only when the condition was classified as unstable.
基金supported by the National High Technology Development Program of China(863Program,Grant No.2008AA092301)the Fundamental Research Foundation of Harbin Engineering University(Grant No.HEUFT08001)the Postdoctoral Science Foundation of China(Grant No.20080440838)
文摘The stability of the motion control system is one of the decisive factors of the control quality for Autonomous Underwater Vehicle(AUV).The divergence of control,which the unstable system may be brought about,is fatal to the operation of AUV.The stability analysis of the PD and S-surface speed controllers based on the Lyapunov's direct method is proposed in this paper.After decoupling the six degree-of-freedom(DOF)motions of the AUV,the axial dynamic behavior is discussed and the condition is deduced,in which the parameters selection within stability domain can guarantee the system asymptotically stable.The experimental results in a tank and on the sea have successfully verified the algorithm reliability,which can be served as a good reference for analyzing other AUV nonlinear control systems.
基金supported by the National Natural Science Fundation of China(No.10972143)
文摘Helical equilibrium of a thin elastic rod has practical backgrounds, such as DNA, fiber, sub-ocean cable, and oil-well drill string. Kirchhoff's kinetic analogy is an effective approach to the stability analysis of equilibrium of a thin elastic rod. The main hypotheses of Kirchhoff's theory without the extension of the centerline and the shear deformation of the cross section are not adoptable to real soft materials of biological fibers. In this paper, the dynamic equations of a rod with a circular cross section are established on the basis of the exact Cosserat model by considering the tension and the shear deformations. Euler's angles are applied as the attitude representation of the cross section. The deviation of the normal axis of the cross section from the tangent of the centerline is considered as the result of the shear deformation. Lyapunov's stability of the helical equilibrium is discussed in static category. Euler's critical values of axial force and torque are obtained. Lyapunov's and Euler's stability conditions in the space domain are the necessary conditions of Lyapunov's stability of the helical rod in the time domain.
基金supported by the National Natural Science Foundation of China (No. 10871063)Scientific Research Fund of Hunan Provincial Education Department (No. 07A038)
文摘In this paper, we investigate the stability of a class of impulsive functional differential equations by using Lyapunov functional and Jensen's inequality. Some new stability theorems are obtained. Examples are given to demonstrate the advantage of the obtained results.
基金Supported by the National Natural Science Founda-tion of China (19531070) and the Major Project Foundation of HubeiProvince Education Department (2004Z001)
文摘Sufficient condition for stochastic unifrom stability of a neutral stochastic functional differential equation is given, especially, new techniques are developed to cope with the neutral delay case, we obtained the sufficient condition for asymptotic stability of neutral stochastic differential delay equations. Due to the new techniques developed in this paper, the results obtained arc very general and useful. The theory developed here gives a unified treatment for various asymptotic estimates e.g. exponential and polynomial bounds.
文摘In this paper, we have discussed the linear stabil- ity analysis of the electrified surface separating two coaxial Oldroyd-B fluid layers confined between two impermeable rigid cylinders in the presence of both interfacial insoluble surfactant and surface charge through porous media. The case of long waves interfacial stability has been studied. The dispersion relation is solved numerically and hence the ef- fects of various parameters are illustrated graphically. Our results reveal that the influence of the physicochemical pa- rameterβ is to shrink the instability region of the surface and reduce the growth rate of the unstable normal modes. Such important effects of the surfactant on the shape of in- terfacial structures are more sensitive to the variation of the βcorresponding to non-Newtonian fluids-model compared with the Newtonian fluids model. In the case of long wave limit, it is demonstrated that increasing r, has a dual role in- fluence (de-stabilizing effects) depending on the viscosity of the core fluid. It has a destabilizing effect at the large values of the core fluid viscosity coefficient, while this role is ex- changed to a regularly stabilizing influence at small values of such coefficient.
基金This work was supported by the National Natural Science Foundation of China(No.11371368)and(No.11871316)。
文摘In this paper,an eco-epidemiological model with Beddington-DeAngelis functional response and a time delay representing the gestation period of the predator is studied.By means of Lyapunov functionals and Laselle’s invariance principle,sufficient conditions are obtained for the global stability of the interior equilibrium and the disease-free equilibrium of the system,respectively.
基金Project(61273095)supported by the National Natural Science Foundation of ChinaProject(135225)supported by the Academy of Finland
文摘To alleviate the conservativeness of the stability criterion for Takagi-Sugeno(T-S)fuzzy time-delay systems,a new delay-dependent stability criterion was proposed by introducing a new augmented Lyapunov function with an additional triple-integral term,which was firstly used to derive the stability criterion for T-S fuzzy time-delay systems.By the same approach,the robust stability issue for fuzzy time-delay systems with uncertain parameters was also considered.On the other hand,in order to enhance the design flexibility,a new design approach for uncertain fuzzy time-delay systems under imperfect premise matching was also proposed,which allows the fuzzy controller to employ different membership functions from the fuzzy time-delay model.By the numerical examples,the proposed stability conditions are less conservative in the sense of getting larger allowable time-delay and obtaining smaller feedback control gains.For instance,when the allowable time-delay increases from 7.3s to 12s for an uncertain T-S fuzzy control system with time-delay,the norm of the feedback gains decreases from(34.299 2,38.560 3)to(10.073 3,11.349 0),respectively.Meanwhile,the effectiveness of the proposed design method was illustrated by the last example with the robustly stable curves of system state under the initial condition ofx(0)=[3-1].
基金Project supported by the National Natural Science Foundation of China (Grant No 10572021) and the Doctoral Program Foundation of Institutions of Higher Education of China (Grant No 20040007022).
文摘The stability of second-order differential equations is studied by using their integrals. A system of second-order differential equations can be considered as a mechanical system with holonomic constraints. A conserved quantity of the mechanical system or a part of the system is obtained by using the Noether theory. It is possible that the conserved quantity becomes a Liapunov function and the stability of the system is proved by the Liapunov theorem.
基金Supported by the the National Natural Science Foundation of China (No.90208003, 30200059) and the Science and Technology Research Foundation of Education Ministry of China (No.02065)
文摘The cellular neural networks with delay (DCNN’s) are investigated, and some new sufficient conditions on asymptotical stability of DCNN’s are derived by constructing the Liapunov functional and utilizing M ? matrixand theω?limit set. It is shown that the new conditions are not related to the delayed parameter.
文摘In this paper, we present a new sufficient condition for absolute stability of Lure system with two additive time-varying delay components. This criterion is expressed as a set of linear matrix inequalities (LMIs), which can be readily tested by using standard numerical software. We use this new criterion to stabilize a class of nonlinear time-delay systems. Some numerical examples are given to illustrate the applicability of the results using standard numerical software.
文摘By using the variational Liapunov method, stability properties in terms of two measures for delay differential equations are discussed. In the case that the unperturbed systems are ordinary differential systems, employing auxiliary measure h*(t, x), criteria on nonuniform and uniform stability in terms of two measures for delay differential equations are established.