充分条件

Firstly, based on the stability criterion for the nominal discrete singular time-delay system, a sufficient condition for the existence of the static output feedback controller in terms of linear matrix inequality with linear matrix equality constraint is established, which ensures that the resulting closed-loop system is regular, causal and robustly asymptotically stable, and the static output feedback controller is designed by the feasible solution of the linear matrix inequality with linear matrix equality constraint.

首先基于标称离散广义时滞系统的稳定条件，以受限线性矩阵不等式形式，得到闭环离散广义时滞系统正则、因果且渐近稳定的充分条件，同时利用受限矩阵不等式的可行解给出静态输出反馈控制器的设计方法；然后采用矩阵的正交补，把求受限线性矩阵不等式的可行解问题转化为求严格线性矩阵不等式的可行解；最后的数值实例说明了所给方法的有效性和正确性。

Based on it, another sufficient condition on asymptotic stability undering the meaning of Lyapunov's is obtained via the method of equivalent transformation and equivalent system.

在此条件基础上，利用等价变换和等价系统的方法，得到了该闭环系统Lyapunov意义下渐近稳定的充分条件。

Then using Positive definite quadratic theory to prove a sufficient condition of Multivariate function's extreme value problem and show some examples about it.

而后利用正定二次型理论，证明了多元函数条件极值的一个充分条件，并给出了其应用的例子。

Under Sturm-Liouville conditions, the existence of at least three positive solutions is proved by using Leggett-Williams fixed point theorem.

利用Leggett-Williams不动点定理，研究了在Sturm-Liouville边界条件下的一类二阶常微分方程组多个正解的存在性，得到了至少三个正解存在的充分条件。

Some sufficient conditions for the forced oscillation of solutions of the equations are obtained using the Robin eigenfunction and the impulsive delay differential inequalities.

考虑一类具强迫项的满足Robin边值条件的脉冲时滞抛物型方程，利用Robin特征函数和脉冲时滞微分不等式获得了这类方程解强迫振动的若干充分条件。

In the second chapter, we consider a kind of Kolmogorov system. The sufficient condition for nonexistence of the closed orbit and existence of the unique and stable limit cycle are obtained by using divergence integral, Poincare-Bendixson theorem and Zhang Zhifenunique theorem.

第二章讨论了一类Kolmogorov系统，利用发散量积分、环域定理和张芷芬唯一性定理，得到了该系统无闭轨的充分条件和存在唯一极限环的条件。

In the second chapter, we consider a kind of Kolmogorov system. The sufficient condition for nonexistence of the closed orbit and existence of the unique and stable limit cycle are obtained by using divergence integral, Poincare-Bendixson theorem and Zhang Zhifen\'unique theorem.

第二章讨论了一类Kolmogorov系统，利用发散量积分、环域定理和张芷芬唯一性定理，得到了该系统无闭轨的充分条件和存在唯一极限环的条件。

Based on the Method of Lyapunov function and interval analysis technique,soMe sufficient conditions of robust absolute stability for the interval Lurie systeM are obtained,which reduces the conservatisM in robustness tests of absolute stability.

用Lyapunov函数方法和区间分析技术，得到了区间Lurie系统鲁棒绝对稳定的一些充分条件，这些条件减少了绝对稳定鲁棒检测的保守性。

At first, we present a necessary condition for the existence of optimal linear state feedback control by means of Lagrange multiplier theorem.

首先利用Lagrange multiplier定理得到了存在最优线性状态反馈解的必要条件，而在加强的条件下也得到了最优控制存在的充分条件。

This system is permanent by comparative principle and globally asymptotically stable through constructing a Liapunov function; for the periodic case, the research has obtained conditions for existence, uniqueness and stability of a positive periodic solution.

利用比较原理研究了系统的持久性，通过构造Liapunov函数证明了系统的全局渐近稳定性，在假设系统为周期系统的条件下得到了正周期解的存在唯一性和全局渐近稳定的充分条件。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。