本文应用李雅普诺夫第二方法与贝尔曼的动态规划法，讨论了最优控制器的分析设计问题，并提出了一种对理论经分析与实际计算都比较方便的序列逼近法。在第一节中，给出了最优控制器分析设计问题的一般提法与作为必要条件的贝尔曼方程。在第二节中，给出了对进一步研究所需的有关李雅普诺夫第二方法的基本结果，以便使以后的论证更为简捷。在第三节中，给出了在一般提法下分析设计问题的一般性结果，其中包括唯一性定理、贝尔曼方程的充分性、序列逼近法及其基本性质。在第四节中，研究了常系数线性系统，解决了最优控制的存在唯一性问题，文中列举了数例，以说明序列逼近法具有较快的收敛速度，并论证了这种方法的收敛速度来按指数进行的。在第五节中，研究了拟常系数线性系统，并分别对缓变系数线性系统与业常拟线性系统进行了讨论，给出了例题以说明理论结果。最后在第六节中，讨论了某些进一步推广的问题。本文所引入的方法，均值接针对综合问题而给出，因而在理论研究与实际运用上，是方便可行的。

In this paper, the robust D stsbility problems are studied by, sine mapping and param-eterization approach. The boundary theorem of robust stability in parameter space is establish-ed, with which we can obtnin some well-known results in robust stability concisely, such as edge theorem. Kharitonov's theorem and diamond theorem for polynomial families. A new approach is presented to judge the D stability of biparameter polynomial family, with which the determination of the largest perturbntion bound of H stable polynomial under given per-turbation patterns (interval model or diamond model) becomes very easy.

The presence of uncertam parameters an a state space or frequency domain description of a linear, time-invariant system manifesis itself as varmbility in the coefficients of the characteristic polynomial. If the famity of all such poly. Nomials is polytodic in coefficient space, we show that the root locations of the entife tamily can be completely determined by examinine only the roots of the porynomuals contained in the exposed edges of the polyiope These proccdutes are compotationally tractabie and this cnterion inipiores upon the prescntly avaitabic stabity tests for uncertain systems. being less ed acvative and explicitly deler. munmg at root locations Equally important is in laci that the results are also applicable to discrete-time systems

The real polynomial f(s)=h(s2)+sg(s2) is Hurwitz if and only if (h, g) forms a so-called 'positive pair' of polynonaials. In this paper, conditions are given that ensure that some polynomials h(2) and g(2) form a positive pair and then it is shown how these results can be applied to the construction of some stability domains. These IIurwitz regions will be exactly described by linear inequalities.

In this paper, an elastic structure model is constructed according to the test data with various confidences and properly selected analytlcal parameters (mass matrix Mor stiffness matrix K). First, the modeong method is dealed, and second, the uniqueness of the result is strictly proved. Finally, a numerical example is given to show the reasonableness of this method and the superiority of the result to that in reference [4].

In this paper Liapunov's second method is applied to the stability for certain functions taking on given values, and some formulae, to estimate the decaying time in the general case, are obtained. The linear system with quasi-constant coefficients, and the quasi-reducible system, are studied in detail.