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TDPDE系统的稳定性涉及到2D拟多项式,TDPDE系统的特征多项式为2D拟多项式,而其零点为一些连续的超曲面,不再是孤立的和可分离的.这导致检验TDPDE系统的稳定性非常困难.为解决上述问题,提出一种检验TDPDE系统渐近稳定性的方法,该方法通过检验TDPDE系统对应的2D特征多项式的Hurwitz稳定性来确定TDPDE系统的渐近稳定性.该文提出的定理建立了TDPDE系统的渐近稳定性与对应的2D特征多项式的Hurwitz稳定性关系,提供了2D特征多项式(2D拟多项式)的Hurwitz稳定性检验方法.由该文结果导出具有简单检验过程的2D拟多项式的Hurwitz-Schur稳定性数值检验算法,并用实例说明其应用.
The stability of TDPDE system involves 2D quasi-polynomials. The characteristic polynomial of TDPDE system is 2D quasi-polynomial, and its zero point is some continuous hypersurfaces, which are no longer isolated and separable. This leads to the verification of the stability of TDPDE system In order to solve the above problems, a method to test the asymptotic stability of TDPDE system is proposed, which verifies the asymptotic stability of the TDPDE system by checking the Hurwitz stability of the corresponding 2D characteristic polynomial in the TDPDE system. The relationship between asymptotic stability of TDPDE system and corresponding Hurwitz stability of 2D characteristic polynomial is established and a Hurwitz stability test method of 2D characteristic polynomial (2D quasi- polynomial) is provided. From the result, a 2D pseudo-test Polynomial Hurwitz-Schur stability numerical test algorithm, and an example to illustrate its application.