This paper presents a novel approach for the numerical solution of differential linear matrix inequalities. The solutions are searched in the class of piecewise-quadratic functions with symmetric matrix coefficients to be determined. To limit the numbers of unknowns, congruence constraints are considered to guarantee continuity of the solution and of its derivative. In Example section, some control problems involving differential linear matrix inequalities are considered and solved in order to compare the proposed approach with alternative approximation methods adopted in the literature.

中文翻译：

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关于微分线性矩阵不等式的数值解

本文提出了一种求解微分线性矩阵不等式的新方法。在具有待确定的对称矩阵系数的分段二次函数类中搜索解。为了限制未知数的数量，考虑同余约束以保证解及其导数的连续性。在示例部分，考虑并解决了一些涉及微分线性矩阵不等式的控制问题，以便将所提出的方法与文献中采用的替代近似方法进行比较。