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The author give ways to construct Liapunov function of a lagrange system with energy consumption: One gives qualitative analysis of the mechanical system, the other gives quantitative estimation as well as qualitative analysis of the asymptotic stability of the studied mechanical system.

论文工作如下:(1)提出了非保守力学系统的李亚普诺夫函数构造途径:定性分析的能量函数方法和可用于定量分析的系统分解方法,并给出了分别使用上述方法的充分性条件。

It obtained analytic expression or arithmetic solution of the mean value, the mean square value, the related function and the spectral density function of heat conduction system of 0-D, 1-D, 2-D and 3-D, by applying stochastically theory of linear system and the results of the first part.

该部分利用线性系统的随机理论和第一部分的成果,获得了0维、1维、2维和3维导热系统均值、均方值、相关函数、谱密度函数的解析表达式或数值解。

The basic idea was to discrete the structure and find the load function according to the energy criterion of buckling and the principle of random displacement method. As the critical load is the minimum of the load function, a problem of frame buckling can be transformed into an optimization problem. Therefore, the critical load can be found through solving the optimization problem.

先将结构离散为一个有限自由度系统;然后根据有限自由度系统平衡稳定性的能量准则和随机位移法的基本原理,建立符合能量准则的载荷函数,该函数不为零的最小值即为临界载荷,由此将稳定问题转化为无约束的多维优化问题;最后应用遗传算法求出相应于最优解的目标函数值。

According to the state equation of dynamic system,the paper puts forward the calculating method of attenuation function of vibration mode by making use of system matrix.

根据运动系统的状态方程,利用系统矩阵得出了振型衰减函数的计算方法,并用衰减函数分析了刚度变化对高振型的影响,从而对地震作用计算中振型数目选取提出了几点有益的建议。

A new kind of algorithm, which is based on Dirac δ-Function, is established by Nonstandard Analysis for M/G/1 queueing system performance gradient estimation with respect to a kind of probability parameter.

新算法在实现过程中需要用样条函数来近似δ函数,但可以同时估计M/G/1排队系统中顾客期望系统时间和忙期期望长度对概率参数的梯度。

The finite-gain stability of the controller was proved under the assumption that the kernel function was local Lipschitz in this open-loop inverse control system. The sufficient condition for that Gaussian kernel function to the local Lipschitz of either variable was given. The stability of the whole system was also proved under some proper assumptions.

针对此开环逆控制系统,在核函数为局部Lipschitz的前提下,证明了控制器是有限增益稳定的,并给出Gaussian核函数对任一变量的局部Lipschitz性的充分条件,在一定合理的假设下给出了控制系统的稳定性结论。

The mathematical orthonormal function is introduced into the structure of filter. Prior information of the system is obtained by mapping the system model to orthonormal basis function.

该滤波器引入正交函数理论,利用系统模型与正交基函数之间的关联,预先获取系统的先验信息,从而兼有FIR和为IIR两者的优点。

For first-order linear DPS with spatial-varying coefficient matrices a method is presented to approximate the system piecewisely by N partial differential equations with constant coefficient matrices.

它包括两大部分,一是关于分布参数系统的频率域数学描述即传递函数这一基本问题的应用研究,二是关于一类用多滞后型传递函数表示的分布系统的控制设计问题。

It is concluded from patch test that the order of interpolation function for pressure must be higher than that of displacement of solid phase.

通过考察系统方程,由分片试验得知压力插值函数的阶必须低于固体相位移插值函数的阶,进而提出了一种系统方程的迭代求解方法。

Secondly, based on the piecewise continuous Lyapunov function andconstant Lyapunov function, the problems of robust guaranteed cost control forparametric uncertain sampled-data control systems are investigated by using the jumpsystem model and linear matrix inequality technique.

然后,针对参数不确定采样系统的鲁棒保性能控制问题,利用跳变模型和线性矩阵不等式技术,分别基于分段连续Lyapunov函数方法和定常Lyapunov函数方法研究了采样系统的鲁棒保性能控制器综合问题。

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