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negative definiteness
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  负定性
     Some theorems for the determination of stability of linear system with the sys-tem matrix are presented. The relation between stability and the generalized negative definiteness of the system matrix is analytically discussed.
     提出了从系统矩阵直接分析线性定常系统稳定性的几个定理,把系统稳定性同系统矩阵的广义负定性联系起来,并进行了分析讨论;
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  相似匹配句对
     From "Negative" to "Positive"
     从消极走向积极
短句来源
     Negative bubbles
     负气泡
短句来源
     On Definiteness and Indefiniteness
     论确定性与不确定性
短句来源
     On the Positive Definiteness of Matrices
     关于矩阵正定性的一些研究
短句来源
     The worry about the negative influence of order idea, emphasizing consistency, continuity and definiteness, will brings to individual and legality.
     对强调一致性、连续性、确定性的秩序观念给个人和法治所可能带来的负面担心绝非多余。
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  negative definiteness
Next the thermodynamic restriction is shown to imply the negative definiteness of the divergence of the energy flux.
      
It is widely known that an estimator for the variogram cannot be used as its representator in some contexts because of its lack of conditional semi negative definiteness.
      
The thermodynamic restrictions on the model parameters are found using the non-negative definiteness of the entropy production.
      
The matrices Pl are obtained by ensuring the negative definiteness of the derivative of the Lyapunov function.
      
This condition gives sufficient condition for negative definiteness of V.
      
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Let r>0 be a given constant, C_n=C([-r,0],R~n). For φ∈C_n, let ||φ|| =sup|φ(s)|, |||φ|||=(integral from n=(-r) to 0(|φ(s)|~2ds))~(1/2). For any given constant H, let C_n~H={φ; φ∈C_n, ||φ||

Let r>0 be a given constant, C_n=C([-r,0],R~n). For φ∈C_n, let ||φ|| =sup|φ(s)|, |||φ|||=(integral from n=(-r) to 0(|φ(s)|~2ds))~(1/2). For any given constant H, let C_n~H={φ; φ∈C_n, ||φ||negative definiteness of the derivative of Liapunov functions along the solutions of (1) in state variables (x,y) can be weakened by the condition of negative definiteness of the derivative of Liapunov funtions along the solutions of (1) in partial state ratable y.

设r>0为一给定常数,C_n=C(〔-r,0〕,R~n).对φ∈C_n,定义‖φ‖=sup|φ(s)|,对任意给定常数H>0,记C~H_m考虑泛函微分方程(t)=F(t,x_t,y_t)(1)■(t)=G(t,x_t,y_t)其中F∈C(t, 0, 0)=0,G(t, 0, 0,)=0_0本文证明文的主要定理中,李雅普诺夫函数沿方程的解的导数关于状态变元(x,y)的定负性条件,可用李雅普诺夫函数沿方程的解的导数仅关于部分状态变元y的定负性条件代替.

Some theorems for the determination of stability of linear system with the sys-tem matrix are presented. The relation between stability and the generalized negative definiteness of the system matrix is analytically discussed. The results show that the stability analysis theorem is consistent with the Liapunov stability theorem for linear systems.

提出了从系统矩阵直接分析线性定常系统稳定性的几个定理,把系统稳定性同系统矩阵的广义负定性联系起来,并进行了分析讨论;结果表明:该分析定理与线性系统的李雅普诺夫稳定性定理是一致的。

It is proved that the set of all symmetric real matrices of order n with eigenvalues lying in the interval(α, β), denoted by Sn(α,β), is convex in Rn×n. With this result, some known results on positive(negative) definiteness, and Hurwitz(Shur) stability, as well as the aperiodic property of polytopes of symmetric matrices are generalized, and a series of insightful necessary and sufficient conditions for some general set of symmetric matrices contained in Sn(α,β) are presented,which are directly...

It is proved that the set of all symmetric real matrices of order n with eigenvalues lying in the interval(α, β), denoted by Sn(α,β), is convex in Rn×n. With this result, some known results on positive(negative) definiteness, and Hurwitz(Shur) stability, as well as the aperiodic property of polytopes of symmetric matrices are generalized, and a series of insightful necessary and sufficient conditions for some general set of symmetric matrices contained in Sn(α,β) are presented,which are directly available for analysis of the positive(negative) definiteness, Hurwitz(Shur) stability and the aperiodic property of a wide class of sets of symmetric matrices.

OnEigenvaluesLocationsofSymmetricMatrixFamiliesDUANGuangren;WANGMinzhi(段广仁,王民智)(Detp.ofControlEngineering,HarbinInsituteofTec...

 
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