共查询到20条相似文献，搜索用时 15 毫秒
1.
In this paper, a finite‐time stability procedure is suggested for a class of Caputo‐Katugampola fractional‐order time delay systems. Sufficient conditions are derived to prove this fact. Numerical results are provided to demonstrate the validity of our theoretical results. 相似文献
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Lei Li 《Asian journal of control》2018,20(1):483-494
This paper discusses first‐ and second‐order fractional‐order PID‐type iterative learning control strategies for a class of Caputo‐type fractional‐order linear time‐invariant system. First, the additivity of the fractional‐order derivative operators is exploited by the property of Laplace transform of the convolution integral, whilst the absolute convergence of the Mittag‐Leffler function on the infinite time interval is induced and some properties of the state transmit function of the fractional‐order system are achieved via the Gamma and Bata function characteristics. Second, by using the above properties and the generalized Young inequality of the convolution integral, the monotone convergence of the developed first‐order learning strategy is analyzed and the monotone convergence of the second‐order learning scheme is derived after finite iterations, when the tracking errors are assessed in the form of the Lebesgue‐p norm. The resultant convergences exhibit that not only the fractional‐order system input and output matrices and the fractional‐order derivative learning gain, but also the system state matrix and the proportional learning gain, and fractional‐order integral learning gain dominate the convergence. Numerical simulations illustrate the validity and the effectiveness of the results. 相似文献
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The bounded input bounded output (BIBO) stability for a nonlinear Caputo fractional system with time‐varying bounded delay and nonlinear output is studied. Utilizing the Razumikhin method, Lyapunov functions and appropriate fractional derivatives of Lyapunov functions some new bounded input bounded output stability criteria are derived. Also, explicit and independent on the initial time bounds of the output are provided. Uniform BIBO stability and uniform BIBO stability with input threshold are studied. A numerical simulation is carried out to show the system's dynamic response, and demonstrate the effectiveness of our theoretical results. 相似文献
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This article provides a comprehensive study on quantitative properties of linear mixed fractional‐order systems with multiple time‐varying delays. The delays can be bounded or unbounded. We first obtain a result on existence and uniqueness of solutions to these systems. Then, we prove a necessary and sufficient condition for their positivity. Finally, we provide a necessary and sufficient criterion to characterize asymptotic stability of positive linear mixed fractional‐order systems with multiple time‐varying delays. 相似文献
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In this paper, we propose algorithms to compute the fractional derivatives of a function by a weighted sum of function values at specified points. The fractional derivatives are considered in the Caputo sense. The error analysis of the algorithms and some illustrative examples are presented. The numerical results confirm that the new algorithms are accurate, efficient and readily implemented. 相似文献
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This article addresses the problem of finite‐time stability (FTS) and finite‐time contractive stability (FTCS) for switched nonlinear time‐delay systems (SNTDSs). By virtues of the Lyapunov‐Razumikhin method, Lyapunov functionals approach, and the comparison principle technique, we obtain some improved Razumikhin‐type theorems that verify FTS and FTCS property for SNTDSs. Moreover, our results allow the estimate of the upper bound of the derivatives for Lyapunov functions to be mode dependent functions which can be positive and negative. Meanwhile, the proposed results also improve the related existing results on the same topic by removing some restrictive conditions. Finally, two examples are presented to verify the effectiveness of our methods. 相似文献
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This paper considers the finite‐time stability of fractional order impulsive switched systems. First, by using the fractional order Lyapunov function, Mittag–Leffler function, and Gronwall–Bellman lemma, two sufficient conditions are given to verify the finite‐time stability of fractional order nonlinear systems. Then, the concept of finite‐time stability is extended to fractional order impulsive switched systems. A sufficient condition is given to verify the finite‐time stability of fractional order impulsive switched systems by combining the method of average dwell time with fractional order Lyapunov function. Finally, two numerical examples are provided to illustrate the theoretical results. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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In this paper, we consider the stability analysis and control synthesis of finite‐time boundedness problems for linear parameter‐varying (LPV) systems subject to parameter‐varying time delays and external disturbances. First, the concepts of uniform finite‐time stability and uniform finite‐time boundedness are introduced to LPV systems. Then, sufficient conditions, which guarantee LPV systems with parameter‐varying time delays finite‐time bounded, are presented by using parameter‐dependent Lyapunov–Krasovskii functionals and free‐weight matrix technologies. Moreover, on the basis of the results on the uniform finite‐time boundedness, the parameter‐dependent state feedback controllers are designed to finite‐time stabilize LPV systems. Both analysis and synthesis conditions are delay‐dependent, and they are formulated in terms of linear matrix inequalities by using efficient interior‐point algorithms. Finally, results obtained in simulation demonstrate the effectiveness of the proposed approach. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
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This paper is concerned with delay‐dependent stability for linear systems with time‐varying delays. By decomposing the delay interval into multiple equidistant subintervals, on which different Lyapunov functionals are chosen, and new Lyapunov‐Krasvskii functionals are then constructed. Employing these new Lyapunov‐Krasvskii functionals, some new delay‐dependent stability criteria are established. The numerical examples show that the obtained results are less conservative than some existing ones in the literature. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
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This paper considers the systematic design of robust stabilizing state feedback controllers for fractional order nonlinear systems with time‐varying delay being possibly unbounded. By using the fractional Halanay inequality and the Caputo fractional derivative of a quadratic function, stabilizability conditions expressed in terms of bilinear matrix inequalities are derived. The controllers can then be obtained by computing the gain matrices. In order to derive the gain matrices, two algorithms are proposed by using the existing computationally linear matrix inequality techniques. Two numerical examples with simulation results are provided to demonstrate the effectiveness of the obtained results. 相似文献
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Xiaozhong Liao 《Asian journal of control》2014,16(6):1891-1896
This paper proposes a computing approach for the delay margin of fractional‐order retarded systems with commensurate time delays. By the Orlando formula, a matrix constructed by the coefficients and commensurate fractional‐order of the characteristic function is defined. By calculating the eigenvalues of this matrix, the existence conditions and computing approach are proposed. If the matrix has some positive real eigenvalues, a finite delay margin exists. If the matrix has no positive real eigenvalue, the delay margin is infinity and the system is stable, independent of the delay margin. Finally, a numerical example and simulation results are given to demonstrate the effectiveness of this approach. 相似文献
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This paper is concerned with establishing robust stability and stabilization criteria for discrete singular time‐delay linear parameter varying (LPV) systems. Firstly, a robust stability criterion is obtained for this class of systems by a delay‐partition approach, and thereby a less conservative sufficient condition which guarantees discrete singular time‐delay LPV systems to be admissible is given. Secondly, a class of state feedback controllers for stabilizing discrete singular time‐delay LPV systems is designed. Finally, compared with existing results, the numerical results of several examples illustrate the effectiveness of the approach proposed in this paper. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society 相似文献
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Semi‐Markovian jump systems are more general than Markovian jump systems in modeling practical systems. On the other hand, the finite‐time stochastic stability is also more effective than stochastic stability in practical systems. This paper focuses on the finite‐time stochastic stability, exponential stochastic stability, and stabilization of semi‐Markovian jump systems with time‐varying delay. First, a new stability condition is presented to guarantee the finite‐time stochastic stability of the system by using a new Lyapunov‐Krasovskii functional combined with Wirtinger‐based integral inequality. Second, the stability criterion is further proved to guarantee the exponential stochastic stability of the system. Moreover, a controller design method is also presented according to the stability criterion. Finally, an example is provided to illustrate that the proposed stability condition is less conservative than other existing results. Additionally, we use the proposed method to design a controller for a load frequency control system to illustrate the effectiveness of the method in a practical system of the proposed method. 相似文献
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In this paper, the delayed state fractional order derivative (DSFOD) is introduced into the existing traditional consensus protocol aiming to improve the robustness of fractional‐order multi‐agent systems against communication time delay. Both of communication channels with time‐delay and without time‐delay cases are considered. Based on the frequency‐domain analysis and algebraic graph theory, it is shown that properly choosing the intensity of DSFOD can improve the robustness of fractional‐order multi‐agent systems against communication delay. Finally, a simulated example with simulations is presented to confirm the correctness and effectiveness of the theoretical results. 相似文献
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In this paper, we study the finite‐time boundedness, stabilization, and L2‐gain for switched positive linear systems (SPLS) with multiple time delays. Using multiple linear copositive Lyapunov functions, sufficient conditions in terms of linear matrix inequalities are obtained for the problems of finite‐time boundedness and stabilization and the design of state feedback controllers for SPLS. Under asynchronous switching, L2‐gain analysis is developed for SPLS under the constraint of average dwell time. Numerical examples are given to illustrate our theoretical results. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
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In this paper, the robust stability of a fractional‐order time‐delay system is analyzed in the frequency domain based on finite spectrum assignment (FSA). The FSA algorithm is essentially an extension of the traditional pole assignment method, which can change the undesirable system characteristic equation into a desirable one. Therefore, the presented analysis scheme can also be used as an alternative time‐delay compensation method. However, it is superior to other time‐delay compensation schemes because it can be applied to open‐loop poorly damped or unstable systems. The FSA algorithm is extended to a fractional‐order version for time‐delay systems at first. Then, the robustness of the proposed algorithm for a fractional‐order delay system is analyzed, and the stability conditions are given. Finally, a simulation example is presented to show the superior robustness and delay compensation performance of the proposed algorithm. Moreover, the robust stability conditions and the time‐delay compensation scheme presented can be applied on both integer‐order and fractional‐order systems. 相似文献
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Dinh Cong Huong 《Asian journal of control》2020,22(3):1127-1137
This paper considers the problem of designing functional interval observers for a class of non‐linear fractional‐order systems with bounded uncertainties. First, interval observers for linear functions of the state vector of the considered system are designed. Then, conditions for the existence of such interval observers are established and an effective algorithm for computing unknown observer matrices is provided in this paper. Finally, numerical examples and simulation results are given to illustrate the effectiveness of the proposed design method. 相似文献
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In this paper, a Galerkin finite element scheme to approximate the time–space fractional diffusion equation is studied. Firstly, the fractional diffusion equation is transformed into a fractional Volterra integro-differential equation. And a second-order fractional trapezoidal formula is used to approach the time fractional integral. Then a Galerkin finite element method is introduced in space direction, where the semi-discretization scheme and fully discrete scheme are given separately. The stability analysis of semi-discretization scheme is discussed in detail. Furthermore, convergence analysis of semi-discretization scheme and fully discrete scheme are given in details. Finally, two numerical examples are displayed to demonstrate the effectiveness of the proposed method. 相似文献