COMPREHENSIVE DAMPING COEFFICIENT——A NEW DEFINITION TO DAMPING EFFECT OF LINEAR TIME-INVARIANT SYSTEMS  

作　　者：李先彬 安立进 

机构地区：[1]Beijing Graduate School of North China Institute of Electric Power

出　　处：《Science China Mathematics》1989年第12期1511-1520,共10页中国科学：数学（英文版）

摘　　要：A new concept is presented to express the damping property of linear time-invariant systems, by the Lyapunov theorem in view of quadratic form-defined energy. Two definitions are introduced: damping energy function D(X_0, X)=Ci∫_(x_0, x) x_idx_(i-1)and comprehensive damping coefficient η-min(Ci/a_(n-i)). It is concluded that (ⅰ) of the Hurwitz determinants, △_(x-1) is proportional to the damping effect of oscillating systems, (ⅱ) the comprehensive damping coefficients of linear time-invariant systems are derived as. piecewise rational fractions which can be easily calculated and (ⅲ) the damping torque coefficient obtained for synchronous machines is independent of ω.A new concept is presented to express the damping property of linear time-invariant systems, by the Lyapunov theorem in view of quadratic form-defined energy. Two definitions are introduced: damping energy function D（X₀, X）=Ci∫_{x₀, x} x_idx_i-1and comprehensive damping coefficient η-min(Ci/a_n-i). It is concluded that （ⅰ） of the Hurwitz determinants, △_x-1 is proportional to the damping effect of oscillating systems, （ⅱ） the comprehensive damping coefficients of linear time-invariant systems are derived as. piecewise rational fractions which can be easily calculated and （ⅲ） the damping torque coefficient obtained for synchronous machines is independent of ω.

关 键 词：LYAPUNOV THEOREM HURWITZ DETERMINANT linear time-invariant system. 

分 类 号：N[自然科学总论]