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中文摘要：
针对非线性控制系统的综合问题，提出了平方和（SOS）方法。SOS方法可以保证所求解的多项式总是非负的。给出了求解SOS问题的广义S方法。作为SOS方法的例子，详细分析了一个非线性系统的吸引域。给出了确定SOS问题中决策变量的方法。讨论了集合包含约束的确定和求解，并讨论了SOS问题求解中的保守性问题。SOS方法为不容易解析求解的非线性问题提供了一个方便的数值求解方法，故本文的方法将会有一个广阔的应用前景。
英文摘要：
A sum-of-squares （SOS） synthesis method is proposed for nonlinear control systems. The SOS method guarantees that the polynomials in solution are always nonnegative. A generalized S - procedure is given for the solution of the SOS problem, The region of attraction of a nonlinear system is analyzed in detail as an example by using the SOS method. The method for declaration of the decision variables of the SOS problem is given. The formation of the set containment constraint and its solution are discussed. The conservativeness of the SOS approach is also discussed. The SOS method provides a numerical easy meth- od for solving an analytically unsolvable nonlinear problem, so the proposed method would have a wide area of applications.
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