Search results for: Lyapunov theorem

Authors: Li Jiang, Baoguang Tian

Abstract:

In this paper, we present the preconditioned mixed-type splitting iterative method for solving the linear systems, Ax = b, where A is a Z-matrix. And we give some comparison theorems to show that the convergence rate of the preconditioned mixed-type splitting iterative method is faster than that of the mixed-type splitting iterative method. Finally, we give a numerical example to illustrate our results.

Keywords: Z-matrix, mixed-type splitting iterative method, precondition, comparison theorem, linear system.

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Authors: Yongkun Li, Kaihong Zhao

Abstract:

By using Mawhin-s continuation theorem of coincidence degree theory, we establish the existence of 2n positive periodic solutions for n species non-autonomous Lotka-Volterra competition systems with harvesting terms. An example is given to illustrate the effectiveness of our results.

Keywords: Positive periodic solutions, Lotka-Volterra competition system, coincidence degree, harvesting term.

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Authors: Qingqing Wang, Shouming Zhong

Abstract:

Utilizing the Lyapunov functional method and combining linear matrix inequality (LMI) techniques and integral inequality approach (IIA) to analyze the global asymptotic stability for delayed neural networks (DNNs),a new sufficient criterion ensuring the global stability of DNNs is obtained.The criteria are formulated in terms of a set of linear matrix inequalities,which can be checked efficiently by use of some standard numercial packages.In order to show the stability condition in this paper gives much less conservative results than those in the literature,numerical examples are considered.

Keywords: Neural networks, Globally asymptotic stability , LMI approach , IIA approach , Time-varying delay.

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Authors: Yongkun Li, Tianwei Zhang, Shufa Bai

Abstract:

By using the method of coincidence degree theory and constructing suitable Lyapunov functional, several sufficient conditions are established for the existence and global exponential stability of anti-periodic solutions for Cohen-Grossberg shunting inhibitory neural networks with delays. An example is given to illustrate our feasible results.

Keywords: Anti-periodic solution, coincidence degree, global exponential stability, Cohen-Grossberg shunting inhibitory cellular neural networks.

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Authors: Changjin Xu, Qianhong Zhang

Abstract:

In this paper, a delayed competitive system with the effect of toxic substances is investigated. With the aid of differential equations with piecewise constant arguments, a discrete analogue of continuous non-autonomous delayed competitive system with the effect of toxic substances is proposed. By using Gaines and Mawhin,s continuation theorem of coincidence degree theory, a easily verifiable sufficient condition for the existence of positive solutions of difference equations is obtained.

Keywords: Competitive system, periodic solution, discrete time delay, topological degree.

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Authors: Zhaohui Wen

Abstract:

In this paper, a food chain model with Holling type II functional response on time scales is investigated. By using the Mawhin-s continuation theorem in coincidence degree theory, sufficient conditions for existence of periodic solutions are obtained.

Keywords: Periodic solutions, food chain model, coincidence degree, time scales.

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Authors: Li Xiguang

Abstract:

In this paper, by constructing a special operator and using fixed point index theorem of cone, we get the sufficient conditions for symmetric positive solution of a class of nonlinear singular boundary value problems with p-Laplace operator, which improved and generalized the result of related paper.

Keywords: Banach space, cone, fixed point index, singular differential equation, p-Laplace operator, symmetric solutions.

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Authors: H. Ifassiouen, M. Guisser, H.Medromi

Abstract:

This paper presents an investigation into the design of a flight control system, using a robust sliding mode control structure, designed using the exact feedback linearization procedure of the dynamic of a small-size autonomous helicopter in hover. The robustness of the controller in the context of stabilization and trajectory tracking with respect to small body forces and air resistance on the main and tail rotor, is analytically proved using Lyapunov approach. Some simulation results are presented to illustrate the performance and robustness of such controller in the presence of small body forces and air resistance.

Keywords: Robust control, sliding mode, stability, Lyapunovapproach.

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Authors: Da-Xue Chen, Guang-Hui Liu

Abstract:

In this paper, we study the oscillation of a class of second-order nonlinear neutral damped variable delay dynamic equations on time scales. By using a generalized Riccati transformation technique, we obtain some sufficient conditions for the oscillation of the equations. The results of this paper improve and extend some known results. We also illustrate our main results with some examples.

Keywords: Oscillation theorem, second-order nonlinear neutral dynamic equation, variable delay, damping, Riccati transformation.

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Authors: Zixin Liu, Jianjun Jiao Wanping Bai

Abstract:

In this paper, the issue of pth moment exponential stability of stochastic recurrent neural network with distributed time delays is investigated. By using the method of variation parameters, inequality techniques, and stochastic analysis, some sufficient conditions ensuring pth moment exponential stability are obtained. The method used in this paper does not resort to any Lyapunov function, and the results derived in this paper generalize some earlier criteria reported in the literature. One numerical example is given to illustrate the main results.

Keywords: Stochastic recurrent neural networks, pth moment exponential stability, distributed time delays.

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Authors: Longqiao Zhou, Zixin Liu, Shu Lü

Abstract:

This paper addresses the robust stability problem of a class of delayed neutral Lur’e systems. Combined with the property of convex function and double integral Jensen inequality, a new tripe integral Lyapunov functional is constructed to derive some new stability criteria. Compared with some related results, the new criteria established in this paper are less conservative. Finally, two numerical examples are presented to illustrate the validity of the main results.

Keywords: Lur’e system, Convex function, Jensen integral inequality, Triple-integral method, Exponential stability.

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Authors: Myeongjin Park, Ohmin Kwon, Juhyun Park, Sangmoon Lee

Abstract:

This paper proposes improved delay-dependent stability conditions of the linear time-delay systems of neutral type. The proposed methods employ a suitable Lyapunov-Krasovskii’s functional and a new form of the augmented system. New delay-dependent stability criteria for the systems are established in terms of Linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. Numerical examples showed that the proposed method is effective and can provide less conservative results.

Keywords: Neutral systems, Time-delay, Stability, Lyapunovmethod, LMI.

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Authors: Li Xiguang

Abstract:

In this paper, by constructing a special operator and using fixed point index theorem of cone, we get the sufficient conditions for symmetric positive solution of a class of nonlinear singular boundary value problems with p-Laplace operator, which improved and generalized the result of related paper.

Keywords: Banach space, cone, fixed point index, singular differential equation, p-Laplace operator, symmetric solutions.

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Authors: Fengxia Zheng

Abstract:

By using two new fixed point theorems for mixed monotone operators, the positive solution of nonlinear fractional differential equation boundary value problem is studied. Its existence and uniqueness is proved, and an iterative scheme is constructed to approximate it.

Keywords: Fractional differential equation, boundary value problem, positive solution, existence and uniqueness, fixed point theorem, mixed monotone operator.

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Authors: Changjin Xu, Peiluan Li

Abstract:

In this paper, we study the stability of a fractional order delayed predator-prey model. By using the Laplace transform, we introduce a characteristic equation for the above system. It is shown that if all roots of the characteristic equation have negative parts, then the equilibrium of the above fractional order predator-prey system is Lyapunov globally asymptotical stable. An example is given to show the effectiveness of the approach presented in this paper.

Keywords: Fractional predator-prey model, laplace transform, characteristic equation.

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Authors: J.H. Park, S. Lakshmanan, H.Y. Jung, S.M. Lee

Abstract:

This paper is concerned with the delay-distributiondependent stability criteria for bidirectional associative memory (BAM) neural networks with time-varying delays. Based on the Lyapunov-Krasovskii functional and stochastic analysis approach, a delay-probability-distribution-dependent sufficient condition is derived to achieve the globally asymptotically mean square stable of the considered BAM neural networks. The criteria are formulated in terms of a set of linear matrix inequalities (LMIs), which can be checked efficiently by use of some standard numerical packages. Finally, a numerical example and its simulation is given to demonstrate the usefulness and effectiveness of the proposed results.

Keywords: BAM neural networks, Probabilistic time-varying delays, Stability criteria.

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Authors: Wookyong Kwon, Sangmoon Lee

Abstract:

In this paper, a sampled-data model predictive tracking control method is presented for mobile robots which is modeled as constrained continuous-time linear parameter varying (LPV) systems. The presented sampled-data predictive controller is designed by linear matrix inequality approach. Based on the input delay approach, a controller design condition is derived by constructing a new Lyapunov function. Finally, a numerical example is given to demonstrate the effectiveness of the presented method.

Keywords: Model predictive control, sampled-data control, linear parameter varying systems, LPV.

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Authors: M. J. Park, S. H. Lee, C. H. Lee, O. M. Kwon

Abstract:

This paper studies a secondary voltage control framework of the microgrids based on the consensus for a communication network of multiagent. The proposed control is designed by the communication network with one-way links. The communication network is modeled by a directed graph. At this time, the concept of sampling is considered as the communication constraint among each distributed generator in the microgrids. To analyze the sampling effects on the secondary voltage control of the microgrids, by using Lyapunov theory and some mathematical techniques, the sufficient condition for such problem will be established regarding linear matrix inequality (LMI). Finally, some simulation results are given to illustrate the necessity of the consideration of the sampling effects on the secondary voltage control of the microgrids.

Keywords: Microgrids, secondary control, multiagent, sampling, LMI.

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Authors: A. Thabet, G. B. H. Frej, M. Boutayeb

Abstract:

This paper presents a design of dynamic feedback control based on observer for a class of large scale Lipschitz nonlinear systems. The use of Differential Mean Value Theorem (DMVT) is to introduce a general condition on the nonlinear functions. To ensure asymptotic stability, sufficient conditions are expressed in terms of linear matrix inequalities (LMIs). High performances are shown through real time implementation with ARDUINO Duemilanove board to the one-link flexible joint robot.

Keywords: Feedback stabilization, DMVT, Lipschitz nonlinear systems, nonlinear observer, real time implementation.

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Authors: M. Pourgholi, V.J.Majd

Abstract:

This paper addresses parameter and state estimation problem in the presence of the perturbation of observer gain bounded input disturbances for the Lipschitz systems that are linear in unknown parameters and nonlinear in states. A new nonlinear adaptive resilient observer is designed, and its stability conditions based on Lyapunov technique are derived. The gain for this observer is derived systematically using linear matrix inequality approach. A numerical example is provided in which the nonlinear terms depend on unmeasured states. The simulation results are presented to show the effectiveness of the proposed method.

Keywords: Adaptive observer, linear matrix inequality, nonlinear systems, nonlinear observer, resilient observer, robust estimation.

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Authors: Yongkun Li, Erliang Xu

Abstract:

In this paper, by using Mawhin-s continuation theorem of coincidence degree theory, we establish the existence of multiple positive periodic solutions of a competitor-competitor-mutualist Lotka-Volterra system with harvesting terms. Finally, an example is given to illustrate our results.

Keywords: Positive periodic solutions, competitor-competitor mutualist Lotka-Volterra systems, coincidence degree, harvesting term.

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Authors: Kaihong Zhao

Abstract:

In this paper, the existence of 2n positive periodic solutions for n species non-autonomous Lotka-Volterra cooperative systems with harvesting terms is established by using Mawhin-s continuation theorem of coincidence degree theory and matrix inequality. An example is given to illustrate the effectiveness of our results.

Keywords: Multiple positive periodic solutions, Nonautonomous Lotka-Volterra cooperative system, Coincidence degree, Harvesting term.

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Authors: Mona Taheri

Abstract:

In this study, we examine multiple algebras and algebraic structures derived from them and by stating a theory on multiple algebras; we will show that the theory of multiple algebras is a natural extension of the theory of universal algebras. Also, we will treat equivalence relations on multiple algebras, for which the quotient constructed modulo them is a universal algebra and will study the basic relation and the fundamental algebra in question. In this study, by stating the characteristic theorem of multiple algebras, we show that the theory of multiple algebras is a natural extension of the theory of universal algebras.

Keywords: multiple algebras , universal algebras

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Authors: Yusuke Onoue, Seiji Fujino, Norimasa Nakashima

Abstract:

The IDR(s) method based on an extended IDR theorem was proposed by Sonneveld and van Gijzen. The original IDR(s) method has excellent property compared with the conventional iterative methods in terms of efficiency and small amount of memory. IDR(s) method, however, has unexpected property that relative residual 2-norm stagnates at the level of less than 10-12. In this paper, an effective strategy for stagnation detection, stagnation avoidance using adaptively information of parameter s and improvement of convergence rate itself of IDR(s) method are proposed in order to gain high accuracy of the approximated solution of IDR(s) method. Through numerical experiments, effectiveness of adaptive tuning IDR(s) method is verified and demonstrated.

Keywords: Krylov subspace methods, IDR(s), adaptive tuning, stagnation of relative residual.

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Authors: K. Raghuwaiya, B. Sharma, J. Vanualailai

Abstract:

This paper presents a set of artificial potential field functions that improves upon, in general, the motion planning and posture control, with theoretically guaranteed point and posture stabilities, convergence and collision avoidance properties of the general3-trailer system in a priori known environment. We basically design and inject two new concepts; ghost walls and the distance optimization technique (DOT) to strengthen point and posture stabilities, in the sense of Lyapunov, of our dynamical model. This new combination of techniques emerges as a convenient mechanism for obtaining feasible orientations at the target positions with an overall reduction in the complexity of the navigation laws. Simulations are provided to demonstrate the effectiveness of the controls laws.

Keywords: Artificial potential fields, 3-trailer systems, motion planning, posture.

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Authors: Khosrow Maleknejad, Reza Mollapourasl, Parvin Torabi, Mahdiyeh Alizadeh,

Abstract:

Sinc-collocation scheme is one of the new techniques used in solving numerical problems involving integral equations. This method has been shown to be a powerful numerical tool for finding fast and accurate solutions. So, in this paper, some properties of the Sinc-collocation method required for our subsequent development are given and are utilized to reduce integral equation of the first kind to some algebraic equations. Then convergence with exponential rate is proved by a theorem to guarantee applicability of numerical technique. Finally, numerical examples are included to demonstrate the validity and applicability of the technique.

Keywords: Integral equation, Fredholm type, Collocation method, Sinc approximation.

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Authors: Ö. Tolga Altınöz

Abstract:

The adaptive backstepping controller for inverted pendulum is designed by using the general motion control model. Backstepping is a novel nonlinear control technique based on the Lyapunov design approach, used when higher derivatives of parameter estimation appear. For easy parameter adaptation, the mathematical model of the inverted pendulum converted into the motion control model. This conversion is performed by taking functions of unknown parameters and dynamics of the system. By using motion control model equations, inverted pendulum is simulated without any information about not only parameters but also measurable dynamics. Also these results are compare with the adaptive backstepping controller which extended with integral action that given from [1].

Keywords: Adaptive backstepping, inverted pendulum, nonlinear adaptive control.

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Authors: Norsinnira Zainul Azlan, Hiroshi Yamaura

Abstract:

This paper presents a new adaptive impedance control strategy, based on Function Approximation Technique (FAT) to compensate for unknown non-flat environment shape or time-varying environment location. The target impedance in the force controllable direction is modified by incorporating adaptive compensators and the uncertainties are represented by FAT, allowing the update law to be derived easily. The force error feedback is utilized in the estimation and the accurate knowledge of the environment parameters are not required by the algorithm. It is shown mathematically that the stability of the controller is guaranteed based on Lyapunov theory. Simulation results presented to demonstrate the validity of the proposed controller.

Keywords: Adaptive impedance control, Function Approximation Technique (FAT), impedance control, unknown environment position.

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Authors: Chen-Yuan Chen, Wan-I Lee, Yi-Chaio Sui, Cheng-Wu Chen

Abstract:

This study focuses on the development of triangular fuzzy numbers, the revising of triangular fuzzy numbers, and the constructing of a HCFN (half-circle fuzzy number) model which can be utilized to perform more plural operations. They are further transformed for trigonometric functions and polar coordinates. From half-circle fuzzy numbers we can conceive cylindrical fuzzy numbers, which work better in algebraic operations. An example of fuzzy control is given in a simulation to show the applicability of the proposed half-circle fuzzy numbers.

Keywords: triangular fuzzy number, half-circle fuzzy numbers, predictions, polar coordinates, Lyapunov method

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Authors: Lianglin Xiong, Yun Zhao, Tao Jiang

Abstract:

In this paper, we study the stability of n-dimensional linear fractional neutral differential equation with time delays. By using the Laplace transform, we introduce a characteristic equation for the above system with multiple time delays. We discover that if all roots of the characteristic equation have negative parts, then the equilibrium of the above linear system with fractional order is Lyapunov globally asymptotical stable if the equilibrium exist that is almost the same as that of classical differential equations. An example is provided to show the effectiveness of the approach presented in this paper.

Keywords: Fractional neutral differential equation, Laplace transform, characteristic equation.

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