周期系数线性系统的稳定性

利用柯西矩阵的性质,讨论了周期系数线性矩阵的稳定性问题.将矩阵稳定的条件减弱为拟稳定,利用矩阵的不等式运算性质,得到了各种周期系统平凡解稳定的判据,所得结论,推广了现有文献的结论.最后,利用Matlab模拟仿真,验证了所得结果的可行性.

On Some Fundamental Theorems in Stability Theory

This paper gives several fundamental theorems for the stability, uniform stability, asymptotic stability and uniform asymptotic stability. Those theorems allow the derivative of Lyapunov functions to be positive on certain sets,relax the restriction about the rate of change of state variable in a system to be bounded in Marachkov's theorem and extend the related results in [4—7].

一种半主动自参数吸振器的设计与分析研究

文中首先研究了由单摆自参数吸振器和主系统组成的两自由度的自参数振动系统,通过理论分析得到了自参数振动系统的解的形式以及半平凡解的稳定边界;其次,为了充分发挥自参数吸振器的吸振能力,提出半主动控制的方法,通过主动调节单摆的摆长,使其摆的固有频率跟踪主系统的外激励的频率;最后,通过数值仿真验证了被动与半主动单摆自参数吸振器对线性主系统的减振效果,仿真结果证明了半主动自参数单摆具有更好的减振性能。

Instability Theorems for Fuzzy Differential Equations

Some instability results of the trivial solution of fuzzy differential equations via Lyapunov functions is elaborated.