Given a stable matrix A∈C<sup>n×n</sup>,there are some simple simultaneous inequalities whosecoefficients rely on A.For （?）P<sup>H</sup>=P∈C<sup>n×n</sup>,if P satisfi...Given a stable matrix A∈C<sup>n×n</sup>,there are some simple simultaneous inequalities whosecoefficients rely on A.For （?）P<sup>H</sup>=P∈C<sup>n×n</sup>,if P satisfies these inequlities,then PA+A<sup>H</sup>P【0.As anapplication of the main results,the stability of the matrix family is treated.Besides,some geometricproperties of the set of all the Lyapunov matrices of a given stable matrix are considered.展开更多
基金This work is supported by the National Natural Science Foundation of China
文摘Given a stable matrix A∈C<sup>n×n</sup>,there are some simple simultaneous inequalities whosecoefficients rely on A.For （?）P<sup>H</sup>=P∈C<sup>n×n</sup>,if P satisfies these inequlities,then PA+A<sup>H</sup>P【0.As anapplication of the main results,the stability of the matrix family is treated.Besides,some geometricproperties of the set of all the Lyapunov matrices of a given stable matrix are considered.
