Virtual synchronous generators(VSGs)are widely introduced to the renewable power generation,the variablespeed pumped storage units,and so on,as a promising gridforming solution.It is noted that VSGs can provide virtua...Virtual synchronous generators(VSGs)are widely introduced to the renewable power generation,the variablespeed pumped storage units,and so on,as a promising gridforming solution.It is noted that VSGs can provide virtual inertia for frequency support,but the larger inertia would worsen the synchronization stability,referring to keeping synchronization with the grid during voltage dips.Thus,this paper presents a transient damping method of VSGs for enhancing the synchronization stability during voltage dips.It is revealed that the loss of synchronization(LOS)of VSGs always accompanies with the positive frequency deviation and the damping is the key factor to remove LOS when the equilibrium point exists.In order to enhance synchronization stability during voltage dips,the transient damping is proposed,which is generated by the frequency deviation in active power loop.Additionally,the proposed method can realize seamless switching between normal state and grid fault.Moreover,detailed control design for transient damping gain is given to ensure the synchronization stability under different inertia requirements during voltage dips.Finally,the experimental results are presented to validate the analysis and the effectiveness of the improved transient damping method.展开更多
In this paper we have established the stability of a generalized nonlinear second-order differential equation in the sense of Hyers and Ulam. We also have proved the Hyers-Ulam stability of Emden-Fowler type equation ...In this paper we have established the stability of a generalized nonlinear second-order differential equation in the sense of Hyers and Ulam. We also have proved the Hyers-Ulam stability of Emden-Fowler type equation with initial conditions.展开更多
This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau equations.The backward Euler method is used for discretizing the temporal derivative of the time-dependent ...This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau equations.The backward Euler method is used for discretizing the temporal derivative of the time-dependent Ginzburg-Landau equations.In this method,the system is decoupled and linearized to avoid solving the non-linear equation at each step.The theoretical analysis proves that the generalized SAV method can preserve the maximum bound principle and energy stability,and this is confirmed by the numerical result,and also shows that the numerical algorithm is stable.展开更多
Owing to their stability,doubly-fed induction generator(DFIG)integrated systems have gained considerable interest and are the most widely implemented type of wind turbines and due to the increasing escalation of the w...Owing to their stability,doubly-fed induction generator(DFIG)integrated systems have gained considerable interest and are the most widely implemented type of wind turbines and due to the increasing escalation of the wind generation penetration rate in power systems.In this study,we investigate a DFIG integrated system comprising four modules:(1)a wind turbine that considers the maximum power point tracking and pitch-angle control,(2)induction generator,(3)rotor/grid-side converter with the corresponding control strategy,and(4)AC power grid.The detailed small-signal modeling of the entire system is performed by linearizing the dynamic characteristic equation at the steady-state value.Furthermore,a dichotomy method is proposed based on the maximum eigenvalue real part function to obtain the critical value of the parameters.Root-locus analysis is employed to analyze the impact of changes in the phase-locked loop,short-circuit ratio,and blade inertia on the system stability.Lastly,the accuracy of the small-signal model and the real and imaginary parts of the calculated dominant poles in the theoretical analysis are verified using PSCAD/EMTDC.展开更多
Stability for the manifolds of equilibrium states of a generalized Birkhoff system is studied. A theorem for the stability of the manifolds of equilibrium states of the general autonomous system is used to the general...Stability for the manifolds of equilibrium states of a generalized Birkhoff system is studied. A theorem for the stability of the manifolds of equilibrium states of the general autonomous system is used to the generalized BirkhoiYian system and two propositions on the stability of the manifolds of equilibrium states of the system are obtained. An example is given to illustrate the application of the results.展开更多
The problem on the stability of motion for a generalized Birkhoffian system was studied. The disturbed equations of motion and their first approximation for the system were established. The criterion of stability of m...The problem on the stability of motion for a generalized Birkhoffian system was studied. The disturbed equations of motion and their first approximation for the system were established. The criterion of stability of motion for the system was set up by using Liapunov's first approximation theory. Based on the theory of Noether symmetry,the Liapunov's function was constructed,and the criterion of stability of motion for the system was also set up by using Liapunov's direct method. Two examples were given to illustrate the application of the results.展开更多
Human activities, such as blasting excavation, bolting, grouting and impounding of reservoirs, will lead to disturbances to rock masses and variations in their structural features and material properties. These engine...Human activities, such as blasting excavation, bolting, grouting and impounding of reservoirs, will lead to disturbances to rock masses and variations in their structural features and material properties. These engineering disturbances are important factors that would alter the natural evolutionary processes or change the multi-field interactions in the rock masses from their initial equilibrium states. The concept of generalized multi-field couplings was proposed by placing particular emphasis on the role of engineering disturbances in traditional multi-field couplings in rock masses. A mathematical model was then developed, in which the effects of engineering disturbances on the coupling-processes were described with changes in boundary conditions and evolutions in thermo-hydro-mechanical (THM) properties of the rocks. A parameter, d, which is similar to damage variables but has a broader physical meaning, was conceptually introduced to represent the degree of engineering disturbances and the couplings among the material properties. The effects of blasting excavation, bolting and grouting in rock engineering were illustrated with various field observations or theoretical results, on which the degree of disturbances and the variations in elastic moduli and permeabilities were particularly focused. The influences of excavation and groundwater drainage on the seepage flow and stability of the slopes were demonstrated with numerical simulations. The proposed approach was further employed to investigate the coupled hydro-mechanical responses of a high rock slope to excavation, bolting and impounding of the reservoir in the dam left abutment of Jinping I hydropower station. The impacts of engineering disturbances on the deformation and stability of the slope during construction and operation were demonstrated.展开更多
The parameters that influence slope stability and their criteria of failure are fairly understood but over-conservative design approaches are often preferred,which can result in excessive overburden removal that may j...The parameters that influence slope stability and their criteria of failure are fairly understood but over-conservative design approaches are often preferred,which can result in excessive overburden removal that may jeopardize profitability in the context of open pit mining.Numerical methods such as finite element and discrete element modelling are instrumental to identify specific zones of stability,but they remain approximate and do not pinpoint the critical factors that influence stability without extensive parametric studies.A large number of degrees of freedom and input parameters may make the outcome of numerical modelling insufficient compared to analytical solutions.Existing analytical approaches have not tackled the stability of slopes using non-linear plasticity criteria and threedimensional failure mechanisms.This paper bridges this gap by using the yield design theory and the Hoek-Brown criterion.Moreover,the proposed model includes the effect of seismic forces,which are not always taken into account in slope stability analyses.The results are presented in the form of rigorous mathematical expressions and stability charts involving the loading conditions and the rock mass properties emanating from the plasticity criterion.展开更多
The nonlinear stability of the three-layer generalized Phillips model, for which the velocity in each layeris constant and the top and bottom surfaces are either rigid or free, is studied by employing Arnol'd'...The nonlinear stability of the three-layer generalized Phillips model, for which the velocity in each layeris constant and the top and bottom surfaces are either rigid or free, is studied by employing Arnol'd'svariational principle and a prior estimate method. The nonlinear stability criteria are established. For comparison, the linear instability criteria are also obtained by using normal mode method. and the influences ofthe free parameter, β parameter and curvature in vertical profile of the horizontal velocity on the linear instability are discussed by use of the growth rate curves. The comparison between the nonlinear stability criterion and the linear one is made. It is shown that insome cases the two criteria are exactly the same in form, but in other cases, they are different. This phenomenon, which reveals the nonlinear property of the linear instability features. is explained by the explosiveresonant interaction (ERI). When there exists the ERI, i.e., the nonlinear mechanisms play a leading role inthe dynamical system. the nonlinear stability criterion is different from the linear one, on the other hand.when there does not exist the ERI. the nonlinear stability criterion is the same as the linear one in form.展开更多
This paper investigates the orbital stability of periodic traveling wave solutions to the generalized Zakharov equations {iu +uxx = uv + |u|^2u, vtt-vxx=(|u|^2)xx.First, we prove the existence of a smooth c...This paper investigates the orbital stability of periodic traveling wave solutions to the generalized Zakharov equations {iu +uxx = uv + |u|^2u, vtt-vxx=(|u|^2)xx.First, we prove the existence of a smooth curve of positive traveling wave solutions of dnoidal type with a fixed fundamental period L for the generalized Zakharov equations. Then, by using the classical method proposed by Benjamin, Bona et al., we show that this solution is orbitally stable by perturbations with period L. The results on the orbital stability of periodic traveling wave solutions for the generalized Zakharov equations in this paper can be regarded as a perfect extension of the results of [15, 16, 19].展开更多
In this article, we introduce the notion of generalized derivations on Hilbert C*-modules. We use a fixed-point method to prove the generalized Hyers-Ulam-Rassias stability associated to the Pexiderized Cauchy-Jensen...In this article, we introduce the notion of generalized derivations on Hilbert C*-modules. We use a fixed-point method to prove the generalized Hyers-Ulam-Rassias stability associated to the Pexiderized Cauchy-Jensen type functional equationrf(x+y/r)+sg(x-y/s)=2h(x)for r, s ∈ R / {0} on Hilbert C*-modules, where f, g, and h are mappings from a Hilbert C*-module M to M.展开更多
In this paper,a sufficient conditions to guarantee the existence and stability of solutions for generalized nonlinear fractional differential equations of orderα(1<α<2)are given.The main results are obtained b...In this paper,a sufficient conditions to guarantee the existence and stability of solutions for generalized nonlinear fractional differential equations of orderα(1<α<2)are given.The main results are obtained by using Krasnoselskii's fixed point theorem in a weighted Banach space.Two examples are given to demonstrate the validity of the proposed results.展开更多
This paper is concerned with the nonlinear stability of planar shock profiles to the Cauchy problem of the generalized KdV-Burgers equation in two dimensions. Our analysis is based on the energy method developed by Go...This paper is concerned with the nonlinear stability of planar shock profiles to the Cauchy problem of the generalized KdV-Burgers equation in two dimensions. Our analysis is based on the energy method developed by Goodman [5] for the nonlinear stability of scalar viscous shock profiles to scalar viscous conservation laws and some new decay estimates on the planar shock profiles of the generalized KdV-Burgers equation.展开更多
Stochastic generalized porous media equation with jump is considered. The aim is to show the moment exponential stability and the almost certain exponential stability of the stochastic equation.
The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was a...The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was analysed for the solution of the generalized system of linear neutral test equations, After the establishment of a sufficient condition for asymptotic stability of the solutions of the generalized system, it is shown that a linear multistep method is NGP(G)-stable if and only if it is A-stable.展开更多
In the interaction of laser-plasma the system of Zakharov equation plays an important role.This system attracted many scientists' wide interest and attention.And the formation, evolution and interaction of the Lan...In the interaction of laser-plasma the system of Zakharov equation plays an important role.This system attracted many scientists' wide interest and attention.And the formation, evolution and interaction of the Langmuir solutions differ from solutions of the KDV equation. Here we consider the following generalized Zakharov展开更多
Inner stability and stabilization of Cohen-Grossberg generalized delay stochastic neural network with distributed parameter are discussed. The main method adopted is, combining inequality techniques, to apply Ito diff...Inner stability and stabilization of Cohen-Grossberg generalized delay stochastic neural network with distributed parameter are discussed. The main method adopted is, combining inequality techniques, to apply Ito differential formula to the constructed average function with respect to spatial variables along the system considered under the integral operator. Some sufficient conditions are given.展开更多
In this paper, equilibrium stability of generalized Birkhoff's autonomous system is discussed. First, equilibrium equations of generalized Birkhoff's autonomous system are set up, and the n the linear approx...In this paper, equilibrium stability of generalized Birkhoff's autonomous system is discussed. First, equilibrium equations of generalized Birkhoff's autonomous system are set up, and the n the linear approximate method and direct method of stability in equilibrium st ate are studied. Some results on equilibrium of generalized Birkhoff's autonomou s system are obtained on the basis of Lyapunov's thorem. Last, the applica tion of the results is illustrated with an example.展开更多
In this paper the definitions of generalized transfer functios of control system and itscontinuity are presented.Using generalized transfer function as a tool,a set of theorems fordeciding movement stability have been...In this paper the definitions of generalized transfer functios of control system and itscontinuity are presented.Using generalized transfer function as a tool,a set of theorems fordeciding movement stability have been constructed.Thus basing understanding of thecharacteristics of a control dynamics system on its measured procedure will simplify thedecision method of movement stability problems.展开更多
In this paper, we first introduce the notion and model of generalized minimax regret equilibria with scalar set payoffs. After that, we study its general stability theorem under the conditions that the existence theor...In this paper, we first introduce the notion and model of generalized minimax regret equilibria with scalar set payoffs. After that, we study its general stability theorem under the conditions that the existence theorem of generalized minimax regret equilibrium point with scalar set payoffs holds. In other words, when the scalar set payoffs functions and feasible constraint mappings are slightly disturbed, by using Fort theorem and continuity results of set-valued mapping optimal value functions, we obtain a general stability theorem for generalized minimax regret equilibria with scalar set payoffs. At the same time, an example is given to illustrate our result.展开更多
文摘Virtual synchronous generators(VSGs)are widely introduced to the renewable power generation,the variablespeed pumped storage units,and so on,as a promising gridforming solution.It is noted that VSGs can provide virtual inertia for frequency support,but the larger inertia would worsen the synchronization stability,referring to keeping synchronization with the grid during voltage dips.Thus,this paper presents a transient damping method of VSGs for enhancing the synchronization stability during voltage dips.It is revealed that the loss of synchronization(LOS)of VSGs always accompanies with the positive frequency deviation and the damping is the key factor to remove LOS when the equilibrium point exists.In order to enhance synchronization stability during voltage dips,the transient damping is proposed,which is generated by the frequency deviation in active power loop.Additionally,the proposed method can realize seamless switching between normal state and grid fault.Moreover,detailed control design for transient damping gain is given to ensure the synchronization stability under different inertia requirements during voltage dips.Finally,the experimental results are presented to validate the analysis and the effectiveness of the improved transient damping method.
文摘In this paper we have established the stability of a generalized nonlinear second-order differential equation in the sense of Hyers and Ulam. We also have proved the Hyers-Ulam stability of Emden-Fowler type equation with initial conditions.
基金supported by the National Natural Science Foundation of China(12126318,12126302).
文摘This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau equations.The backward Euler method is used for discretizing the temporal derivative of the time-dependent Ginzburg-Landau equations.In this method,the system is decoupled and linearized to avoid solving the non-linear equation at each step.The theoretical analysis proves that the generalized SAV method can preserve the maximum bound principle and energy stability,and this is confirmed by the numerical result,and also shows that the numerical algorithm is stable.
基金supported by the Key Laboratory of Modern Power System Simulation and Control&Renewable Energy Technology,Ministry of Education(Northeast Electric Power University),Jilin 132012,China(MPSS2023-06).
文摘Owing to their stability,doubly-fed induction generator(DFIG)integrated systems have gained considerable interest and are the most widely implemented type of wind turbines and due to the increasing escalation of the wind generation penetration rate in power systems.In this study,we investigate a DFIG integrated system comprising four modules:(1)a wind turbine that considers the maximum power point tracking and pitch-angle control,(2)induction generator,(3)rotor/grid-side converter with the corresponding control strategy,and(4)AC power grid.The detailed small-signal modeling of the entire system is performed by linearizing the dynamic characteristic equation at the steady-state value.Furthermore,a dichotomy method is proposed based on the maximum eigenvalue real part function to obtain the critical value of the parameters.Root-locus analysis is employed to analyze the impact of changes in the phase-locked loop,short-circuit ratio,and blade inertia on the system stability.Lastly,the accuracy of the small-signal model and the real and imaginary parts of the calculated dominant poles in the theoretical analysis are verified using PSCAD/EMTDC.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10772025,10932002 and 10972127)the Natural Science Foundation of Henan Province,China(Grant No.102300410144)the Beijing Municipal Key Disciplines Fund for General Mechanics and Foundation of Mechanics,China
文摘Stability for the manifolds of equilibrium states of a generalized Birkhoff system is studied. A theorem for the stability of the manifolds of equilibrium states of the general autonomous system is used to the generalized BirkhoiYian system and two propositions on the stability of the manifolds of equilibrium states of the system are obtained. An example is given to illustrate the application of the results.
基金Sponsored by the National Natural Science Foundation of China( 10972151)the Natural Science Foundation of Higher Education Institution of Jiangsu Province,China ( 08KJB130002)
文摘The problem on the stability of motion for a generalized Birkhoffian system was studied. The disturbed equations of motion and their first approximation for the system were established. The criterion of stability of motion for the system was set up by using Liapunov's first approximation theory. Based on the theory of Noether symmetry,the Liapunov's function was constructed,and the criterion of stability of motion for the system was also set up by using Liapunov's direct method. Two examples were given to illustrate the application of the results.
基金Supported by the National Natural Science Fund for Distinguished Young Scholars of China(50725931)the National Natural Science Foundation of China(50839004,51079107)the Supporting Program of the "Eleventh Five-year Plan" for Sci & Tech Research of China(2008BAB29B01)
文摘Human activities, such as blasting excavation, bolting, grouting and impounding of reservoirs, will lead to disturbances to rock masses and variations in their structural features and material properties. These engineering disturbances are important factors that would alter the natural evolutionary processes or change the multi-field interactions in the rock masses from their initial equilibrium states. The concept of generalized multi-field couplings was proposed by placing particular emphasis on the role of engineering disturbances in traditional multi-field couplings in rock masses. A mathematical model was then developed, in which the effects of engineering disturbances on the coupling-processes were described with changes in boundary conditions and evolutions in thermo-hydro-mechanical (THM) properties of the rocks. A parameter, d, which is similar to damage variables but has a broader physical meaning, was conceptually introduced to represent the degree of engineering disturbances and the couplings among the material properties. The effects of blasting excavation, bolting and grouting in rock engineering were illustrated with various field observations or theoretical results, on which the degree of disturbances and the variations in elastic moduli and permeabilities were particularly focused. The influences of excavation and groundwater drainage on the seepage flow and stability of the slopes were demonstrated with numerical simulations. The proposed approach was further employed to investigate the coupled hydro-mechanical responses of a high rock slope to excavation, bolting and impounding of the reservoir in the dam left abutment of Jinping I hydropower station. The impacts of engineering disturbances on the deformation and stability of the slope during construction and operation were demonstrated.
文摘The parameters that influence slope stability and their criteria of failure are fairly understood but over-conservative design approaches are often preferred,which can result in excessive overburden removal that may jeopardize profitability in the context of open pit mining.Numerical methods such as finite element and discrete element modelling are instrumental to identify specific zones of stability,but they remain approximate and do not pinpoint the critical factors that influence stability without extensive parametric studies.A large number of degrees of freedom and input parameters may make the outcome of numerical modelling insufficient compared to analytical solutions.Existing analytical approaches have not tackled the stability of slopes using non-linear plasticity criteria and threedimensional failure mechanisms.This paper bridges this gap by using the yield design theory and the Hoek-Brown criterion.Moreover,the proposed model includes the effect of seismic forces,which are not always taken into account in slope stability analyses.The results are presented in the form of rigorous mathematical expressions and stability charts involving the loading conditions and the rock mass properties emanating from the plasticity criterion.
文摘The nonlinear stability of the three-layer generalized Phillips model, for which the velocity in each layeris constant and the top and bottom surfaces are either rigid or free, is studied by employing Arnol'd'svariational principle and a prior estimate method. The nonlinear stability criteria are established. For comparison, the linear instability criteria are also obtained by using normal mode method. and the influences ofthe free parameter, β parameter and curvature in vertical profile of the horizontal velocity on the linear instability are discussed by use of the growth rate curves. The comparison between the nonlinear stability criterion and the linear one is made. It is shown that insome cases the two criteria are exactly the same in form, but in other cases, they are different. This phenomenon, which reveals the nonlinear property of the linear instability features. is explained by the explosiveresonant interaction (ERI). When there exists the ERI, i.e., the nonlinear mechanisms play a leading role inthe dynamical system. the nonlinear stability criterion is different from the linear one, on the other hand.when there does not exist the ERI. the nonlinear stability criterion is the same as the linear one in form.
基金supported by the National Natural Science Foundation of China(11401122)Science and technology project of Qufu Normal University(xkj201607)
文摘This paper investigates the orbital stability of periodic traveling wave solutions to the generalized Zakharov equations {iu +uxx = uv + |u|^2u, vtt-vxx=(|u|^2)xx.First, we prove the existence of a smooth curve of positive traveling wave solutions of dnoidal type with a fixed fundamental period L for the generalized Zakharov equations. Then, by using the classical method proposed by Benjamin, Bona et al., we show that this solution is orbitally stable by perturbations with period L. The results on the orbital stability of periodic traveling wave solutions for the generalized Zakharov equations in this paper can be regarded as a perfect extension of the results of [15, 16, 19].
文摘In this article, we introduce the notion of generalized derivations on Hilbert C*-modules. We use a fixed-point method to prove the generalized Hyers-Ulam-Rassias stability associated to the Pexiderized Cauchy-Jensen type functional equationrf(x+y/r)+sg(x-y/s)=2h(x)for r, s ∈ R / {0} on Hilbert C*-modules, where f, g, and h are mappings from a Hilbert C*-module M to M.
文摘In this paper,a sufficient conditions to guarantee the existence and stability of solutions for generalized nonlinear fractional differential equations of orderα(1<α<2)are given.The main results are obtained by using Krasnoselskii's fixed point theorem in a weighted Banach space.Two examples are given to demonstrate the validity of the proposed results.
文摘This paper is concerned with the nonlinear stability of planar shock profiles to the Cauchy problem of the generalized KdV-Burgers equation in two dimensions. Our analysis is based on the energy method developed by Goodman [5] for the nonlinear stability of scalar viscous shock profiles to scalar viscous conservation laws and some new decay estimates on the planar shock profiles of the generalized KdV-Burgers equation.
基金Project supported by the Tianyuan Foundation of National Natural Science of China(No.11126079)the China Postdoctoral Science Foundation(No.2013M530559)the Fundamental Research Funds for the Central Universities(No.CDJRC10100011)
文摘Stochastic generalized porous media equation with jump is considered. The aim is to show the moment exponential stability and the almost certain exponential stability of the stochastic equation.
文摘The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was analysed for the solution of the generalized system of linear neutral test equations, After the establishment of a sufficient condition for asymptotic stability of the solutions of the generalized system, it is shown that a linear multistep method is NGP(G)-stable if and only if it is A-stable.
基金The research is supported by the Scientific Research Foundation of Yunnan Provincial Departmentthe Natural Science Foundation of Yunnan Province(No.2005A0026M).
文摘In the interaction of laser-plasma the system of Zakharov equation plays an important role.This system attracted many scientists' wide interest and attention.And the formation, evolution and interaction of the Langmuir solutions differ from solutions of the KDV equation. Here we consider the following generalized Zakharov
文摘Inner stability and stabilization of Cohen-Grossberg generalized delay stochastic neural network with distributed parameter are discussed. The main method adopted is, combining inequality techniques, to apply Ito differential formula to the constructed average function with respect to spatial variables along the system considered under the integral operator. Some sufficient conditions are given.
文摘In this paper, equilibrium stability of generalized Birkhoff's autonomous system is discussed. First, equilibrium equations of generalized Birkhoff's autonomous system are set up, and the n the linear approximate method and direct method of stability in equilibrium st ate are studied. Some results on equilibrium of generalized Birkhoff's autonomou s system are obtained on the basis of Lyapunov's thorem. Last, the applica tion of the results is illustrated with an example.
文摘In this paper the definitions of generalized transfer functios of control system and itscontinuity are presented.Using generalized transfer function as a tool,a set of theorems fordeciding movement stability have been constructed.Thus basing understanding of thecharacteristics of a control dynamics system on its measured procedure will simplify thedecision method of movement stability problems.
文摘In this paper, we first introduce the notion and model of generalized minimax regret equilibria with scalar set payoffs. After that, we study its general stability theorem under the conditions that the existence theorem of generalized minimax regret equilibrium point with scalar set payoffs holds. In other words, when the scalar set payoffs functions and feasible constraint mappings are slightly disturbed, by using Fort theorem and continuity results of set-valued mapping optimal value functions, we obtain a general stability theorem for generalized minimax regret equilibria with scalar set payoffs. At the same time, an example is given to illustrate our result.