This paper shows that first integrals of discrete equation of motion for Birkhoff systems can be determined explicitly by investigating the invariance properties of the discrete Pfaffian. The result obtained is a disc...This paper shows that first integrals of discrete equation of motion for Birkhoff systems can be determined explicitly by investigating the invariance properties of the discrete Pfaffian. The result obtained is a discrete analogue of theorem of Noether in the calculus of variations. An example is given to illustrate the application of the results.展开更多
In this paper, we investigate the nonlinear fractional difference equation with nonlocal fractional boundary conditions. We derive the Green's function for this problem and show that it satisfies certain propertie...In this paper, we investigate the nonlinear fractional difference equation with nonlocal fractional boundary conditions. We derive the Green's function for this problem and show that it satisfies certain properties. Some existence results are obtained by means of nonlinear alternative of Leray-Schauder type theorem and Krasnosel-skii's fixed point theorem.展开更多
Gain based predistorter (PD) is a highly effective and simple digital baseband predistorter which compensates for the nonlinear distortion of PAs. Lookup table (LUT) is the core of the gain based PD. This paper presen...Gain based predistorter (PD) is a highly effective and simple digital baseband predistorter which compensates for the nonlinear distortion of PAs. Lookup table (LUT) is the core of the gain based PD. This paper presents a discrete Newton’s method based adaptive technique to modify LUT. We simplify and convert the hardship of adaptive updating LUT to the roots finding problem for a system of two element real equations on athematics. And we deduce discrete Newton’s method based adaptive iterative formula used for updating LUT. The iterative formula of the proposed method is in real number field, but secant method previously published is in complex number field. So the proposed method reduces the number of real multiplications and is implemented with ease by hardware. Furthermore, computer simulation results verify gain based PD using discrete Newton’s method could rectify nonlinear distortion and improve system performance. Also, the simulation results reveal the proposed method reaches to the stable statement in fewer iteration times and less runtime than secant method.展开更多
A robust stabilization problem is considered for time delay nonlinear discrete-time systems based on T-S fuzzy model. A necessary and sufficient condition for the existence of such controllers is given through Lyapuno...A robust stabilization problem is considered for time delay nonlinear discrete-time systems based on T-S fuzzy model. A necessary and sufficient condition for the existence of such controllers is given through Lyapunov stability theorem. And it is further shown that this condition is equivalent to the solvability of a certain linear matrix inequality, which can be solved easily by using the LMI toolbox of Matlab. At last, an illustrative example of truck-trailer is presented to show the feasibility and effectiveness of the proposed method.展开更多
This paper is concerned with the problem of stabilization of the Roesser type discrete-time nonlinear 2-D system that plays an important role in many practical applications. First, a discrete-time 2-D T-S fuzzy model ...This paper is concerned with the problem of stabilization of the Roesser type discrete-time nonlinear 2-D system that plays an important role in many practical applications. First, a discrete-time 2-D T-S fuzzy model is proposed to represent the underlying nonlinear 2-D system. Second, new quadratic stabilization conditions are proposed by applying relaxed quadratic stabilization technique for 2-D case. Third, for sake of further reducing conservatism, new non-quadratic stabilization conditions are also proposed by applying a new parameter-dependent Lyapunov function, matrix transformation technique, and relaxed technique for the underlying discrete-time 2-D T-S fuzzy system. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.展开更多
Warehousing and transferring strategies are an important part of business operations. The issue of optimal warehousing and transferring strategy is studied in this paper. Wal-Mart in Wuhan serves as an example to esta...Warehousing and transferring strategies are an important part of business operations. The issue of optimal warehousing and transferring strategy is studied in this paper. Wal-Mart in Wuhan serves as an example to establish a (s, S) random storage strategy model, a Markov chain model, and a nonlinear discrete programming model, aiming at maximizing the profit per cycle of every branch and further maximizing the company’s total profit per cycle. Among them, the random storage strategy model establishes a security zone of inventory for every branch, that is, it can meet consumers’ demand without spending too much storage costs. The Markov chain model is used to get the probability of losing sales opportunities in every branch. The nonlinear discrete programming model takes into account the horizontal transferring among branches, which further maximizes the company’s overall profit expectations. The three models above can be used to formulate inventory strategies, assess risks, and provide advice for every branch in order to form a complete storage ecosystem and provide constructive suggestions for the company’s operations.展开更多
In this paper, we present a new integration algorithm based on the discrete Pfaff-Birkhoff principle for Birkhoffian systems. It is proved that the new algorithm can preserve the general symplectic geometric structure...In this paper, we present a new integration algorithm based on the discrete Pfaff-Birkhoff principle for Birkhoffian systems. It is proved that the new algorithm can preserve the general symplectic geometric structures of Birkhoffian systems. A numerical experiment for a damping oscillator system is conducted. The result shows that the new algorithm can better simulate the energy dissipation than the R-K method, which illustrates that we can numerically solve the dynamical equations by the discrete variational method in a Birkhoffian framework for the systems with a general symplectic structure. Furthermore, it is demonstrated that the results of the numerical experiments are determined not by the constructing methods of Birkhoffian functions but by whether the numerical method can preserve the inherent nature of the dynamical system.展开更多
The robust H∞ control problem of norm bounded uncertain discrete Takagi-Sugeno (T-S) fuzzy systems with state delay is addressed. First, by constructing an appropriate basis-dependent Lyapunov-Krasovskii function, ...The robust H∞ control problem of norm bounded uncertain discrete Takagi-Sugeno (T-S) fuzzy systems with state delay is addressed. First, by constructing an appropriate basis-dependent Lyapunov-Krasovskii function, a new delay-dependent sufficient condition on robust H∞-disturbance attenuation is presented, in which both robust stability and prescribed H∞ performance are guaranteed to be achieved. Then based on the condition, a delay-dependent robust Hoo controller design scheme is developed in term of a convex algorithm. Finally, examples are given to illustrate the effectiveness of the proposed method.展开更多
Fractional sine series(FRSS)and fractional cosine series(FRCS)are the discrete form of the fractional cosine transform(FRCT)and fractional sine transform(FRST).The recent stud-ies have shown that discrete convolution ...Fractional sine series(FRSS)and fractional cosine series(FRCS)are the discrete form of the fractional cosine transform(FRCT)and fractional sine transform(FRST).The recent stud-ies have shown that discrete convolution is widely used in optics,signal processing and applied mathematics.In this paper,firstly,the definitions of fractional sine series(FRSS)and fractional co-sine series(FRCS)are presented.Secondly,the discrete convolution operations and convolution theorems for fractional sine and cosine series are given.The relationship of two convolution opera-tions is presented.Lastly,the discrete Young’s type inequality is established.The proposed theory plays an important role in digital filtering and the solution of differential and integral equations.展开更多
The discrete logarithm problem(DLP)is to find a solution n such that g^n=h in a finite cyclic group G=,where h∈G.The DLP is the security foundation of many cryptosystems,such as RSA.We propose a method to improve Pol...The discrete logarithm problem(DLP)is to find a solution n such that g^n=h in a finite cyclic group G=,where h∈G.The DLP is the security foundation of many cryptosystems,such as RSA.We propose a method to improve Pollard’s kangaroo algorithm,which is the classic algorithm for solving the DLP.In the proposed algorithm,the large integer multiplications are reduced by controlling whether to perform large integer multiplication.To control the process,the tools of expanding factor and jumping distance are introduced.The expanding factor is an indicator used to measure the probability of collision.Large integer multiplication is performed if the value of the expanding factor is greater than the given bound.The improved algorithm requires an average of(1.633+o(1))q(1/2)times of the large integer multiplications.In experiments,the average large integer multiplication times is approximately(1.5+o(1))q(1/2).展开更多
In this work we study two types of Discrete Hill’s equation. The first comes from the discretization process of a Continuous-time Hill’s equation, we called Discretized Hill’s equation. The Second is a naturally ob...In this work we study two types of Discrete Hill’s equation. The first comes from the discretization process of a Continuous-time Hill’s equation, we called Discretized Hill’s equation. The Second is a naturally obtained in Discrete-Time and will be called Discrete-time Hill’s equation. The objective of discretization is preserving the continuous-time behavior and we show this property. On the contrary a completely different dynamic property was found for the Discrete-Time Hill’s equation. At the end of the paper is shown that both types share the nonoscillatory behavior of solutions in the 0-th Arnold Tongue.展开更多
A new computational algorithm is introduced for solving scattering problem in periodic structure. The PML technique is used to deal with the difficulty on truncating the unbounded domain while the DSC algorithm is uti...A new computational algorithm is introduced for solving scattering problem in periodic structure. The PML technique is used to deal with the difficulty on truncating the unbounded domain while the DSC algorithm is utilized for the spatial discretization. The present study reveals that the method is efficient for solving the problem.展开更多
In this article, we report the derivation of high accuracy finite difference method based on arithmetic average discretization for the solution of Un=F(x,u,u′)+∫K(x,s)ds , 0 x s < 1 subject to natural boundary co...In this article, we report the derivation of high accuracy finite difference method based on arithmetic average discretization for the solution of Un=F(x,u,u′)+∫K(x,s)ds , 0 x s < 1 subject to natural boundary conditions on a non-uniform mesh. The proposed variable mesh approximation is directly applicable to the integro-differential equation with singular coefficients. We need not require any special discretization to obtain the solution near the singular point. The convergence analysis of a difference scheme for the diffusion convection equation is briefly discussed. The presented variable mesh strategy is applicable when the internal grid points of the solution space are both even and odd in number as compared to the method discussed by authors in their previous work in which the internal grid points are strictly odd in number. The advantage of using this new variable mesh strategy is highlighted computationally.展开更多
The problems of stability and stabilization for the discrete Takagi-Sugeno(T-S) fuzzy time-delay system are investigated.By constructing a discrete piecewise Lyapunov-Krasovskii function(PLKF) in each maximal over...The problems of stability and stabilization for the discrete Takagi-Sugeno(T-S) fuzzy time-delay system are investigated.By constructing a discrete piecewise Lyapunov-Krasovskii function(PLKF) in each maximal overlapped-rules group(MORG),a new sufficient stability condition for the open-loop discrete T-S fuzzy time-delay system is proposed and proved.Then the systematic design of the fuzzy controller is investigated via the parallel distributed compensation control scheme,and a new stabilization condition for the closed-loop discrete T-S fuzzy time-delay system is proposed.The above two sufficient conditions only require finding common matrices in each MORG.Compared with the common Lyapunov-Krasovskii function(CLKF) approach and the fuzzy Lyapunov-Krasovskii function(FLKF) approach,these proposed sufficient conditions can not only overcome the defect of finding common matrices in the whole feasible region but also largely reduce the number of linear matrix inequalities to be solved.Finally,simulation examples show that the proposed PLKF approach is effective.展开更多
In this paper a novel technique, Authentication and Secret Message Transmission using Discrete Fourier Transformation (ASMTDFT) has been proposed to authenticate an image and also some secret message or image can be t...In this paper a novel technique, Authentication and Secret Message Transmission using Discrete Fourier Transformation (ASMTDFT) has been proposed to authenticate an image and also some secret message or image can be transmitted over the network. Instead of direct embedding a message or image within the source image, choosing a window of size 2 x 2 of the source image in sliding window manner and then con-vert it from spatial domain to frequency domain using Discrete Fourier Transform (DFT). The bits of the authenticating message or image are then embedded at LSB within the real part of the transformed image. Inverse DFT is performed for the transformation from frequency domain to spatial domain as final step of encoding. Decoding is done through the reverse procedure. The experimental results have been discussed and compared with the existing steganography algorithm S-Tools. Histogram analysis and Chi-Square test of source image with embedded image shows the better results in comparison with the S-Tools.展开更多
This article deals with the robust stability analysis and passivity of uncertain discrete-time Takagi- Sugeno (T-S) fuzzy systems with time delays. The T-S fuzzy model with parametric uncertainties can approximate n...This article deals with the robust stability analysis and passivity of uncertain discrete-time Takagi- Sugeno (T-S) fuzzy systems with time delays. The T-S fuzzy model with parametric uncertainties can approximate nonlinear uncertain systems at any precision. A sufficient condition on the existence of robust passive controller is established based on the Lyapunov stability theory. With the help of linear matrix inequality (LMI) method, robust passive controllers are designed so that the closed-loop system is robust stable and strictly passive. Furthermore, a convex optimization problem with LMI constraints is formulated to design robust passive controllers with the maximum dissipation rate. A numerical example illustrates the validity of the proposed method.展开更多
Time-delays,due to the information transmission between subsystems,naturally exist in large-scale systems and the existence of the delay is frequently a source of instability. This paper considers the problems of robu...Time-delays,due to the information transmission between subsystems,naturally exist in large-scale systems and the existence of the delay is frequently a source of instability. This paper considers the problems of robust non-fragile fuzzy control for a class of uncertain discrete nonlinear large-scale systems with time-delay and controller gain perturbations described by T-S fuzzy model. An equivalent T-S fuzzy model is represented for discrete-delay nonlinear large-scale systems. A sufficient condition for the existence of such non-fragile controllers is further derived via the Lyapunov function and the linear matrix inequality( LMI) approach. Simulation results demonstrate the feasibility and the effectiveness of the proposed design and the proper stabilization of the system in spite of controller gain variations and uncertainties.展开更多
基金Project partially supported by the National Natural Science Foundation of China (Grant No 10172056) and the Science Research of the Education Bureau of Anhui Province, China (Grant No 2006KJ263B). Acknowledgement We wish to thank the referees for their careful reading of the manuscript and their useful remarks which helped us to improve the quality of this paper.
文摘This paper shows that first integrals of discrete equation of motion for Birkhoff systems can be determined explicitly by investigating the invariance properties of the discrete Pfaffian. The result obtained is a discrete analogue of theorem of Noether in the calculus of variations. An example is given to illustrate the application of the results.
基金Supported by the National Natural Science Foundation of China(11161049)
文摘In this paper, we investigate the nonlinear fractional difference equation with nonlocal fractional boundary conditions. We derive the Green's function for this problem and show that it satisfies certain properties. Some existence results are obtained by means of nonlinear alternative of Leray-Schauder type theorem and Krasnosel-skii's fixed point theorem.
文摘Gain based predistorter (PD) is a highly effective and simple digital baseband predistorter which compensates for the nonlinear distortion of PAs. Lookup table (LUT) is the core of the gain based PD. This paper presents a discrete Newton’s method based adaptive technique to modify LUT. We simplify and convert the hardship of adaptive updating LUT to the roots finding problem for a system of two element real equations on athematics. And we deduce discrete Newton’s method based adaptive iterative formula used for updating LUT. The iterative formula of the proposed method is in real number field, but secant method previously published is in complex number field. So the proposed method reduces the number of real multiplications and is implemented with ease by hardware. Furthermore, computer simulation results verify gain based PD using discrete Newton’s method could rectify nonlinear distortion and improve system performance. Also, the simulation results reveal the proposed method reaches to the stable statement in fewer iteration times and less runtime than secant method.
基金Supported by National Natural Science Foundation of P. R. China (60274009)
文摘A robust stabilization problem is considered for time delay nonlinear discrete-time systems based on T-S fuzzy model. A necessary and sufficient condition for the existence of such controllers is given through Lyapunov stability theorem. And it is further shown that this condition is equivalent to the solvability of a certain linear matrix inequality, which can be solved easily by using the LMI toolbox of Matlab. At last, an illustrative example of truck-trailer is presented to show the feasibility and effectiveness of the proposed method.
基金Supported by National Natural Science Foundation of China (50977008, 60904017, 60774048, 60728307), the Funds for Creative Research Groups of China (60521003), the Program for Cheung Kong Scholars and Innovative Research Team in University (IRT0421), and the 111 Project (B08015), National High Technology Research and Development Program of China (863 Program) (2006AA04Z183)
文摘This paper is concerned with the problem of stabilization of the Roesser type discrete-time nonlinear 2-D system that plays an important role in many practical applications. First, a discrete-time 2-D T-S fuzzy model is proposed to represent the underlying nonlinear 2-D system. Second, new quadratic stabilization conditions are proposed by applying relaxed quadratic stabilization technique for 2-D case. Third, for sake of further reducing conservatism, new non-quadratic stabilization conditions are also proposed by applying a new parameter-dependent Lyapunov function, matrix transformation technique, and relaxed technique for the underlying discrete-time 2-D T-S fuzzy system. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.
文摘Warehousing and transferring strategies are an important part of business operations. The issue of optimal warehousing and transferring strategy is studied in this paper. Wal-Mart in Wuhan serves as an example to establish a (s, S) random storage strategy model, a Markov chain model, and a nonlinear discrete programming model, aiming at maximizing the profit per cycle of every branch and further maximizing the company’s total profit per cycle. Among them, the random storage strategy model establishes a security zone of inventory for every branch, that is, it can meet consumers’ demand without spending too much storage costs. The Markov chain model is used to get the probability of losing sales opportunities in every branch. The nonlinear discrete programming model takes into account the horizontal transferring among branches, which further maximizes the company’s overall profit expectations. The three models above can be used to formulate inventory strategies, assess risks, and provide advice for every branch in order to form a complete storage ecosystem and provide constructive suggestions for the company’s operations.
基金supported by the National Natural Science Foundation of China(Grant Nos.11301350,11172120,and 11202090)the Liaoning University Prereporting Fund Natural Projects(Grant No.2013LDGY02)
文摘In this paper, we present a new integration algorithm based on the discrete Pfaff-Birkhoff principle for Birkhoffian systems. It is proved that the new algorithm can preserve the general symplectic geometric structures of Birkhoffian systems. A numerical experiment for a damping oscillator system is conducted. The result shows that the new algorithm can better simulate the energy dissipation than the R-K method, which illustrates that we can numerically solve the dynamical equations by the discrete variational method in a Birkhoffian framework for the systems with a general symplectic structure. Furthermore, it is demonstrated that the results of the numerical experiments are determined not by the constructing methods of Birkhoffian functions but by whether the numerical method can preserve the inherent nature of the dynamical system.
文摘The robust H∞ control problem of norm bounded uncertain discrete Takagi-Sugeno (T-S) fuzzy systems with state delay is addressed. First, by constructing an appropriate basis-dependent Lyapunov-Krasovskii function, a new delay-dependent sufficient condition on robust H∞-disturbance attenuation is presented, in which both robust stability and prescribed H∞ performance are guaranteed to be achieved. Then based on the condition, a delay-dependent robust Hoo controller design scheme is developed in term of a convex algorithm. Finally, examples are given to illustrate the effectiveness of the proposed method.
基金supported by the National Natural Science Foundation of China(Nos.61861044,62001193,11961072 and 62041212)The Natural Science Foundation of Shaanxi Province(Nos.2020JM-547 and 2020JM-548)the Sci-ence Foundation of Yan’an University(Nos.YDY2017-05 and YDBK2018-36).
文摘Fractional sine series(FRSS)and fractional cosine series(FRCS)are the discrete form of the fractional cosine transform(FRCT)and fractional sine transform(FRST).The recent stud-ies have shown that discrete convolution is widely used in optics,signal processing and applied mathematics.In this paper,firstly,the definitions of fractional sine series(FRSS)and fractional co-sine series(FRCS)are presented.Secondly,the discrete convolution operations and convolution theorems for fractional sine and cosine series are given.The relationship of two convolution opera-tions is presented.Lastly,the discrete Young’s type inequality is established.The proposed theory plays an important role in digital filtering and the solution of differential and integral equations.
基金partially supported by National Key R&D Program of China(no.2017YFB0802500)The 13th Five-Year National Cryptographic Development Foundation(no.MMJJ20180208)+1 种基金Beijing Science and Technology Commission(no.2181100002718001)NSF(no.61272039).
文摘The discrete logarithm problem(DLP)is to find a solution n such that g^n=h in a finite cyclic group G=,where h∈G.The DLP is the security foundation of many cryptosystems,such as RSA.We propose a method to improve Pollard’s kangaroo algorithm,which is the classic algorithm for solving the DLP.In the proposed algorithm,the large integer multiplications are reduced by controlling whether to perform large integer multiplication.To control the process,the tools of expanding factor and jumping distance are introduced.The expanding factor is an indicator used to measure the probability of collision.Large integer multiplication is performed if the value of the expanding factor is greater than the given bound.The improved algorithm requires an average of(1.633+o(1))q(1/2)times of the large integer multiplications.In experiments,the average large integer multiplication times is approximately(1.5+o(1))q(1/2).
文摘In this work we study two types of Discrete Hill’s equation. The first comes from the discretization process of a Continuous-time Hill’s equation, we called Discretized Hill’s equation. The Second is a naturally obtained in Discrete-Time and will be called Discrete-time Hill’s equation. The objective of discretization is preserving the continuous-time behavior and we show this property. On the contrary a completely different dynamic property was found for the Discrete-Time Hill’s equation. At the end of the paper is shown that both types share the nonoscillatory behavior of solutions in the 0-th Arnold Tongue.
基金Supported by the NNSF of China(10626017)the Science Foundation of the Education Committee of Heilongjiang Province(11511276)the Foundation of Heilongjiang Province(LBH-Q05114).
文摘A new computational algorithm is introduced for solving scattering problem in periodic structure. The PML technique is used to deal with the difficulty on truncating the unbounded domain while the DSC algorithm is utilized for the spatial discretization. The present study reveals that the method is efficient for solving the problem.
文摘In this article, we report the derivation of high accuracy finite difference method based on arithmetic average discretization for the solution of Un=F(x,u,u′)+∫K(x,s)ds , 0 x s < 1 subject to natural boundary conditions on a non-uniform mesh. The proposed variable mesh approximation is directly applicable to the integro-differential equation with singular coefficients. We need not require any special discretization to obtain the solution near the singular point. The convergence analysis of a difference scheme for the diffusion convection equation is briefly discussed. The presented variable mesh strategy is applicable when the internal grid points of the solution space are both even and odd in number as compared to the method discussed by authors in their previous work in which the internal grid points are strictly odd in number. The advantage of using this new variable mesh strategy is highlighted computationally.
基金supported in part by the Scientific Research Project of Heilongjiang Province Education Bureau(12541200)
文摘The problems of stability and stabilization for the discrete Takagi-Sugeno(T-S) fuzzy time-delay system are investigated.By constructing a discrete piecewise Lyapunov-Krasovskii function(PLKF) in each maximal overlapped-rules group(MORG),a new sufficient stability condition for the open-loop discrete T-S fuzzy time-delay system is proposed and proved.Then the systematic design of the fuzzy controller is investigated via the parallel distributed compensation control scheme,and a new stabilization condition for the closed-loop discrete T-S fuzzy time-delay system is proposed.The above two sufficient conditions only require finding common matrices in each MORG.Compared with the common Lyapunov-Krasovskii function(CLKF) approach and the fuzzy Lyapunov-Krasovskii function(FLKF) approach,these proposed sufficient conditions can not only overcome the defect of finding common matrices in the whole feasible region but also largely reduce the number of linear matrix inequalities to be solved.Finally,simulation examples show that the proposed PLKF approach is effective.
文摘In this paper a novel technique, Authentication and Secret Message Transmission using Discrete Fourier Transformation (ASMTDFT) has been proposed to authenticate an image and also some secret message or image can be transmitted over the network. Instead of direct embedding a message or image within the source image, choosing a window of size 2 x 2 of the source image in sliding window manner and then con-vert it from spatial domain to frequency domain using Discrete Fourier Transform (DFT). The bits of the authenticating message or image are then embedded at LSB within the real part of the transformed image. Inverse DFT is performed for the transformation from frequency domain to spatial domain as final step of encoding. Decoding is done through the reverse procedure. The experimental results have been discussed and compared with the existing steganography algorithm S-Tools. Histogram analysis and Chi-Square test of source image with embedded image shows the better results in comparison with the S-Tools.
基金supported by the National Natural Science Foundation of China(60710002)Self-Planned Task of State Key Laboratory of Robotics and System(SKLRS200801A03).
文摘This article deals with the robust stability analysis and passivity of uncertain discrete-time Takagi- Sugeno (T-S) fuzzy systems with time delays. The T-S fuzzy model with parametric uncertainties can approximate nonlinear uncertain systems at any precision. A sufficient condition on the existence of robust passive controller is established based on the Lyapunov stability theory. With the help of linear matrix inequality (LMI) method, robust passive controllers are designed so that the closed-loop system is robust stable and strictly passive. Furthermore, a convex optimization problem with LMI constraints is formulated to design robust passive controllers with the maximum dissipation rate. A numerical example illustrates the validity of the proposed method.
文摘Time-delays,due to the information transmission between subsystems,naturally exist in large-scale systems and the existence of the delay is frequently a source of instability. This paper considers the problems of robust non-fragile fuzzy control for a class of uncertain discrete nonlinear large-scale systems with time-delay and controller gain perturbations described by T-S fuzzy model. An equivalent T-S fuzzy model is represented for discrete-delay nonlinear large-scale systems. A sufficient condition for the existence of such non-fragile controllers is further derived via the Lyapunov function and the linear matrix inequality( LMI) approach. Simulation results demonstrate the feasibility and the effectiveness of the proposed design and the proper stabilization of the system in spite of controller gain variations and uncertainties.