Semi-definite programming and functional inequalities for distributed parameter systems
Semi-definite programming and functional inequalities for distributed parameter systems
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分布式参数系统的半定规划和函数不等式
DOI：
10.1109/cdc.2014.7040060
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
A. Papachristodoulou
中科院分区：
文献类型：
--
作者：
G. Valmórbida;M. Ahmadi;A. Papachristodoulou
我们研究有界域上具有二次被积函数的一维积分不等式。这些不等式成立的条件是根据函数矩阵不等式来表述的，而函数矩阵不等式必须在积分域中成立。对于多项式函数矩阵的情况，矩阵不等式为正性的充分条件以及积分不等式的充分条件被转换为半定程序。这些不等式用于研究线性偏微分方程的稳定性。
We study one-dimensional integral inequalities on bounded domains, with quadratic integrands. Conditions for these inequalities to hold are formulated in terms of function matrix inequalities which must hold in the domain of integration. For the case of polynomial function matrices, sufficient conditions for positivity of the matrix inequality and, therefore, for the integral inequalities are cast as semi-definite programs. The inequalities are used to study stability of linear partial differential equations.