共查询到20条相似文献，搜索用时 468 毫秒
1.
函数凹凸性是一种重要的几何性质,函数的凹凸性也是高等数学的一个基本内容。函数的凹凸性是证明比较复杂不等式和构造不等式的有力工具。文章给出了函数凹凸性的定义以及判别方法,进一步探讨了函数凹凸性在证明不等式和构造不等式中的具体应用。 相似文献
2.
F.M. Reza 《Journal of The Franklin Institute》1982,313(2):97-105
A fundamental theorem and inequalities were derived earlier by the author describing arithmetic-geometric means and convex behaviour of the active energy dissipated by arbitrary linear reciprocal passive systems. These results are extended to give a new global theorem concerning bounds of energy for arbitrary linear active or passive, reciprocal or non-reciprocal systems. 相似文献
3.
F.M. Reza 《Journal of The Franklin Institute》1983,316(3):279-290
A new theorem expands the domain of the scalar immittance functions Z(p) to the operator Z(T) where T(s) is an invertible linear passive n-port system. Elements R, L, C of Z(p) are replaced by operators RI, LT, and [CT] - 1. All frequency transformations may be considered contained in this theorem when T is a scalar. 相似文献
4.
This paper presents a constructive method to design a cooperative state and output feedback to steer a group of nonholonomic mobile robots in chained form to form a desired geometric formation shape. The control methodology divides the resulting tracking error dynamics into a cascaded of linear and time-varying subsystems. A basic consensus algorithm is first applied to the linear subsystem which makes the states synchronize exponentially to zero. Once this first linear subsystem has converged, the second cascade can be treated as a linear time-varying subsystem perturbed by a vanishing term from its cascade. A dynamic state and output feedback is constructed to achieve synchronization of the rest of the states. The proof of stability is given using a result from cascade systems. Since time delay appears in many interconnection networks and particularly in cooperative control, its effect on the stability of the closed-loop system is analyzed using Razumikhim theorem. It is shown that the established cooperative controller work well even in the presence of time delay. Numerical simulations are performed on models of car-like mobile robots to show the effectiveness of the proposed cooperative state and output-feedback controllers. 相似文献
5.
物联网三元空间域中传播动力学的形成与演化机制 总被引：1，自引：0，他引：1
基于物联网环境下"人(H)-机(M)-物(T)"3类主体所对应的{用户需求域,信息空间域,物理空间域}的三元体系架构,以及贯穿其间的{控制流,数据流,感知流}的动态交互模式,按照"模式构建—决策分析—形态推演"逐层递进的分析思路提出物联网三元空间域的传播动力学模型,从而定量刻画三元网络空间中传播行为的发生发展过程以及由此形成的系统演化状态;最后基于物联传播的模拟仿真环境,对其传播动力学特性进行算例分析。实验研究结果符合预期,验证了传播决策模型的合理性。 相似文献
6.
J.C. Dunn 《Journal of The Franklin Institute》1973,295(2):117-133
If T maps a convex domain DT into itself, and if {ωn} is a real sequence with range in (0, 1] then the recursive averaging process, generates a sequence {x?n}; with range in DT. Under suitable conditions on DT, T and {ωn} the sequence {x?n} will converge in some sense to a fixed point of T. We prove that if DT is a closed convex subset of a complex Hilbert space H, if Tω = (1 ? ω) I + ωT is a strict contraction for some ω ? (0, 1], and if {ωn} satisfies the conditions, and then, for arbitrary ξ ? DT, {x?n} converges strongly to (the unique) fixed point of T. We also prove that if DT and {ωn} satisfy the foregoing conditions, if T has at least one fixed point, and if Tω is non-expansive for some ω ? (0, 1], then for all ξ ? DT, {x?n} converges at least weakly to some fixed point of T. Finally, we apply these results to linear equations involving bounded normal operators and obtain an extension of the classical Neumann operator series. 相似文献
7.
The problem of nontrivial bounds of moments of inertia for plane configurations is formulated. The Winternitz theorem is generalized to establish the bounds of the ratio of the Nth moment of areas of two subdomains created by any of the centroidal axes of a convex domain. For convex equi-area domains the upper bound of the minimum moment of inertia with respect to a general coordinate system is discussed. In particular, for the cases of the origin of coordinate axes coinciding with the centroid and coinciding with a point on the periphery, the upper bound of the minimum moment of inertia is proved to belong to an equilateral triangle and an isosceles 120° triangle, respectively. 相似文献
8.
Jiangrong Li Zhiguang Feng Yuxin Zhao Juan Shi 《Journal of The Franklin Institute》2018,355(13):5721-5735
The problem of reachable set estimation is studied for discrete-time bilinear system in this paper. Time-varying delays and bounded input disturbances are both considered in bilinear system. The aim is to find reachable set that converges from all the states of system with initial conditions. By constructing Lyapunov–Krasovskii functional, sufficient delay-dependent less conservative stable conditions of reachable set estimation are obtained for bilinear delay system via the reciprocally convex combination and delay partition approaches. The derived theorem can guarantee that all the states of system with initial conditions from some domain are bounded in an ellipsoid and all the states from other domain are converged exponentially within a ball. One simulation example is presented to illustrate the correctness of the derived result in this paper. 相似文献
9.
基于参数相关Lyapunov泛函不确定时滞系统的鲁棒稳定性 总被引：3，自引：0，他引：3
研究了含多面体不确定性的时滞系统的鲁棒稳定性问题。利用参数相关的Lyapunov泛函,得到了基于LMI的时滞系统时滞相关的鲁棒稳定的充分条件。在该条件中不确定系统在多面体不同的顶点用不同的Lyapunov阵判断其稳定性,而已有的结果为在所有的顶点用一个共同Lyapunov阵分析。进一步,将确定系统稳定的最大时滞问题转化为求广义特征值的拟凸优化问题。最后数值例子说明了该方法有较小的保守性 相似文献
10.
M.O. Ahmad C.H. Reddy V. Ramachandran M.N.S. Swamy 《Journal of The Franklin Institute》1979,307(2):71-81
Necessary and sufficient conditions are obtained for the realization of an m-variable positive real function (PRF) as the impedence function of a resistively-terminated ladder network of m lossless two-ports connected in cascade. Each two-port is a single-variable lossless ladder with all of its transmission zeros either at the origin or at finity. Conditions are also obtained when each of the two-ports is a Fujisawa-type lowpass ladder. 相似文献
11.
《Journal of The Franklin Institute》2023,360(14):10517-10535
Variable fractional-order (VFO) differential equations are a beneficial tool for describing the nonlinear behavior of complex dynamical phenomena. In comparison with the constant FO derivatives, it describes the memory properties of such systems that can vary in the time domain and spatial location. This article investigates the stability and stabilization of VFO neutral systems in the presence of time-varying structured uncertainties and time-varying delay. FO Lyapunov theorem is adopted to achieve order-dependent and delay-dependent criteria for both nominal and uncertain VFO neutral delay systems. The obtained conditions are given in respect of linear matrix inequality by designing a delayed state feedback controller. Simulations verify the main results. 相似文献
12.
M.O. Ahmad C.H. Reddy V. Ramachandran M.N.S. Swamy 《Journal of The Franklin Institute》1979,307(6):315-329
Some partial derivative properties of the impedance function of a resistively-terminated network which is a cascade of m lossless two-ports of variables p1 to pm dre established. Those cases where some of the lossless two-ports are lowpass or highpass ladder networks with all of their transmission zeros at the origin or at infinity are also examined. Necessary and sufficient conditions involving partial derivatives and under which an m-variable reactance or positive real function can be realized as the impedance function of a pi-variable lowpass or highpass ladder network, with all of its transmission zeros at pi = 0 or pi = ∞, and terminated in a reactance or positive real impedance function in the other variables are derived. 相似文献
13.
14.
黄秦安 《科学技术与辩证法》2010,(6):22-25
在形式主义学派数学哲学基本主张中,元叙事、基础主义和绝对主义构成了其现代性的思想特质。哥德尔不完全性定理表明,形式化证明对于论证数学真理是不充分的,这构成了拒绝形式主义的主要理由。伴随着基础主义思想的衰落,形式主义的整体数学观走到了其历史发展的终点。 相似文献
15.
This paper proposes a new wave digital filter derived from doubly terminated LC-ladder networks by replacing each series or shunt arm element of the ladder by its equivalent digital two-port. It is shown that such two-ports may be cascaded without the use of adapters defined by Fettweis (1). A number of realizations of the wave digital two-ports, which are canonic with respect to both multipliers and delays, have been obtained. Also a realization which is canonic with respect to multipliers only is given and an example considered using this realization. The sensitivity of this filter with respect to the multiplier coefficient changes due to finite word length is compared with the conventional cascaded digital filter and also the one proposed by Renner and Gupta. It is found that the proposed filter appears to be a more desirable form of implementation than the conventional cascade form and comparable to that of Renner and Gupta (2). 相似文献
16.
《Journal of The Franklin Institute》2023,360(9):6402-6424
This paper is concerned with the problems of set-based finite-time stability (SFTS) and set-based finite-time boundedness (SFTB) for both certain and uncertain linear time-varying systems. The concepts of SFTS and SFTB are defined. Different from existing results, sufficient conditions for SFTS and SFTB are directly derived from the basic definitions of finite-time stability (FTS) and finite-time boundedness (FTB) by using the convex hull technique rather than utilizing the weighted quadratic functions. Thus, more practical constraints on the system states can be dealt with. Furthermore, intervals, zonotopes and polytopes are employed to describe the typical compact convex sets. For linear uncertain systems, the uncertain time-varying state sets are assumed to be represented by interval matrices and matrix zonotopes, respectively. Finally, numerical examples are provided to illustrate the effectiveness of the main results. 相似文献
17.
高振龙 《中国科学院研究生院学报》2011,28(1):5-11
利用截尾方法在一定尾概率条件下得到了三角阵列{Xn,j;1≤j≤kn,n≥1}的中偏差,其中{kn;n≥1}是一列严格单调递增的正整数且对任意的正整数n,{Xn,j;1≤j≤kn}是独立同分布的. 相似文献
18.
人口发展是影响家庭生活基本能耗及碳排放的重要因素,而生活用能作为终端能源消费对总能源的消费结构、供求关系和节能减排具有重要影响。本文基于STIRPAT模型,运用中国1997-2010年30个省份的动态及静态面板数据模型,分析了城镇化进程中不同地区人口发展与家庭生活基本能耗及碳排放的关系。结果表明,人均消费水平成为导致家庭生活基本能耗和碳排放升高主要的影响因子,而提高电力使用百分比和城镇化率抑制其增长。老龄化率及家庭规模在城镇化过程中对家庭生活基本能耗及碳排放的影响有着不同的作用。 相似文献
19.
In this paper, the approximation problem of T–S fuzzy linear singular system for a class of nonlinear singular system with derivative of input is considered and the nonlinear singular system has impulses. Consider a numerical example and a two-wheel drive robot, the T–S fuzzy singular systems are calculated for original system with derivative of input. According to solvability and steps of solving of the two examples, the results are extended to more generally nonlinear singular system with derivative of input. The theorem and algorithm that are given if input-state system is bounded impulse-free item and separable impulse item, it can be approximated by T–S fuzzy singular system with arbitrary accuracy. Finally, a numerical simulation is carried out to show the consistency with theoretical analysis and illustrate the effectiveness of approximation. 相似文献
20.
Mohamed Serry 《Journal of The Franklin Institute》2021,358(6):3215-3231
In this paper, a method to under-approximate finite-time reachable sets and tubes for a class of continuous-time linear uncertain systems is proposed. The class under consideration is the linear time-varying (LTV) class with time-varying integrable system matrices and uncertain initial and input values belonging to known convex compact sets. The proposed method depends upon the iterative use of constant-input reachable sets, which results in convergent under-approximations in the sense of the Hausdorff distance. As a consequence of the convergence, it is shown that interior points of reachable sets are attainable using piecewise constant inputs. The computational complexity of a zonotopic implementation of the proposed method is discussed and comparisons with existing under-approximation methods are established. Finally, the proposed approach is illustrated through two numerical examples. 相似文献