充分条件

In this paper,we study the existence.uniqueness and asymptotic stability of the periodic solutions for a class of nonautonomous systems by using the method of Liapunov Function.

利用Liapunov函数方法，研究了一类非自治系统周期解的存在唯一性及渐近稳定性，得到了存在唯一渐近稳定的周期解的充分条件。

In this paper, the boundedness and stability of solutions for a class of fourth order nonlinear differential equations are studied by using the method of Liapunov function.

本文利用Liapunov函数方法，研究了一类四阶非线性微分方程解的稳定性及有界性，得出了解的有界性及稳定性存在的充分条件。

By constructing a Liapunov function, we obtain some sufficient conditions which ensure the persistence of the first system, and the existence of periodic solutions of the second system which is established by using coincidence degree theory.

另外，我们也利用重合度理论得到了第二个系统正周期解存在的充分条件。

By using Mawhin\'s continuous theorem and liapunov function, sufficient conditions for the existence and globally asymptotic stability of positive periodic solutions of three systems are derived, respectively.

我们还利用Mawhin连续性定理分别建立了两个系统正周期解存在的充分条件。

This sufficient condition can be expressed in a form of linear matrix inequality for easy verification.

该充分条件可表示为一个线性矩阵不等式的形式，进而易于验证。

Linear Fractional Transformation is adopted to translate the control of perturbation to the control of disturbance, then cost index is augmented, and with the min-max method, a robust receding horizon control law is derived. The sufficient conditions for the existence of the control law and closed-loop stability are also presented. The result is extended to time-invariant system with an infinite horizon, and its consistence with the robust control based on the concept of Quadratic Stability is verified.

首先利用线性分式变换，将摄动系统的鲁棒控制问题转化为对扰动系统的鲁棒控制问题；然后通过对性能指标的扩展，利用min-max方法，得到了鲁棒滚动时域控制律，并给出了其存在和使闭环系统渐近稳定的充分条件，并将结果扩展到对定常系统时域无穷的的情况，指出其与现有的基于二次型稳定概念提出的鲁棒控制的一致性。

Firstly, Receding horizon H〓 control based on state feedback with terminal constraints is proposed for systems with disturbance inputs and parameter perturbations. Linear Fractional Transformation and some existed results on Receding horizon H〓 control for systems without perturbations are introduced.

首先针对同时存在外界输入扰动和自身参数摄动的不确定线性时变系统，利用线性分式变换和现有的一些无摄动系统滚动时域H〓控制的结果，得到了基于状态反馈的终端约束滚动时域H〓控制器的设计方法，并给出了控制律存在和使闭环系统渐近稳定的充分条件。

Based on the proposed performance criterion, a sufficient condition for the existence of gain-scheduled H2/H(subscript ∞) filter is derived. Furthermore, the filter design problem is converted into a convex optimization problem with linear matrix inequality constraints.

基于该性能准则，推导了变增益H2/H滤波器存在的充分条件，并将滤波器设计问题转化为具有线性矩阵不等式约束的凸优化问题。

By using methods of passivity and switching control of states of the linear subsystem, both stabilization of the linear subsystem and invariance of the specified region in state space can be guaranteed simultaneously. Hence, a sufficient condition for the robust invariance switching control of this class of systems was derived.

通过基于鲁棒严格无源技术和线性子系统状态反馈的切换控制来镇定线性子系统，同时保证了指定区域的正不变性，从而得到了该类系统鲁棒不变切换控制的充分条件。

The control objective is achieved by firstly using robust passivity to stabilize the linear subsystem, and then with resort to switching control technique to guarantee the invariance of the specified region in state space simultaneously. Hence, a sufficient condition for the robust invariance switching control of this class of systems is derived.

控制思想是首先通过鲁棒无源性技术来镇定线性子系统，再借助切换控制技术得到系统轨迹对于指定区域的正不变性，从而得到了该类系统鲁棒不变切换控制的充分条件。

She gently rebuff ed him, but agreed that they could be friends

她婉言拒绝了，但同意作为朋友相处。

If in the penal farm, you were sure to be criticized.

要是在劳改农场，你等着挨绳子吧！