This paper proposes a method to ascertain the stability of two dimensional linear time invariant discrete system within the shifted unit circle which is represented by the form of characteristic equation. Further an e...This paper proposes a method to ascertain the stability of two dimensional linear time invariant discrete system within the shifted unit circle which is represented by the form of characteristic equation. Further an equivalent single dimensional characteristic equation is formed from the two dimensional characteristic equation then the stability formulation in the left half of Z-plane, where the roots of characteristic equation f(Z) = 0 should lie within the shifted unit circle. The coefficient of the unit shifted characteristic equation is suitably arranged in the form of matrix and the inner determinants are evaluated using proposed Jury’s concept. The proposed stability technique is simple and direct. It reduces the computational cost. An illustrative example shows the applicability of the proposed scheme.展开更多
The earthquakes with Ms≥6.0 are often gathered into belts or clusters and are roughly consistent with tectonic structure trends in the Sichuan-Yunnan (Chuan-Dian) region. The middle south part(98°-106°E, 21...The earthquakes with Ms≥6.0 are often gathered into belts or clusters and are roughly consistent with tectonic structure trends in the Sichuan-Yunnan (Chuan-Dian) region. The middle south part(98°-106°E, 21°-34°N) of South-North Seismic Zone can be zoned into seven small areas. There all were strong quakes with M_s≥7.0 historically in each small area. Ten earthquakes with M_s≥7.0 have occurred in this region since 1970 and they appeared in five small areas respectively. The relationships between occurrence-time and cumulative frequencies of strong quakes in these five areas are shown to be an exponential distribution or power function. By examining the inner coincidence it is indicated that these relationships are of definite significance to mid-long term macroseismic prediction of each area.展开更多
文摘This paper proposes a method to ascertain the stability of two dimensional linear time invariant discrete system within the shifted unit circle which is represented by the form of characteristic equation. Further an equivalent single dimensional characteristic equation is formed from the two dimensional characteristic equation then the stability formulation in the left half of Z-plane, where the roots of characteristic equation f(Z) = 0 should lie within the shifted unit circle. The coefficient of the unit shifted characteristic equation is suitably arranged in the form of matrix and the inner determinants are evaluated using proposed Jury’s concept. The proposed stability technique is simple and direct. It reduces the computational cost. An illustrative example shows the applicability of the proposed scheme.
文摘The earthquakes with Ms≥6.0 are often gathered into belts or clusters and are roughly consistent with tectonic structure trends in the Sichuan-Yunnan (Chuan-Dian) region. The middle south part(98°-106°E, 21°-34°N) of South-North Seismic Zone can be zoned into seven small areas. There all were strong quakes with M_s≥7.0 historically in each small area. Ten earthquakes with M_s≥7.0 have occurred in this region since 1970 and they appeared in five small areas respectively. The relationships between occurrence-time and cumulative frequencies of strong quakes in these five areas are shown to be an exponential distribution or power function. By examining the inner coincidence it is indicated that these relationships are of definite significance to mid-long term macroseismic prediction of each area.
