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本文研究了区间变时滞广义系统的时滞依赖稳定性问题,即寻求稳定判据保证广义系统的正则性、无脉冲性和渐近稳定性。通过利用一个新的Lyapunov-Krasovskii泛函和自由权矩阵方法,得到了该系统渐近稳定的时滞依赖新判据。所提出的泛函,能充分利用区间时滞的上界、下界和这两个界中间值的信息。新判据以线性矩阵不等式形式给出,很容易利用MATLAB验证。数值算例表明,与参考文献中的方法相比,本文结果可获得较大的允许时滞上界,这也验证了方法的有效性。
In this paper, we study the problem of time-dependent stability of a generalized system with time-varying time-varying delays, ie, finding the stability criterion to guarantee the regularity, impulsiveness and asymptotic stability of the generalized system. By using a new Lyapunov-Krasovskii functional and free-weight matrix method, a new criterion of asymptotic stability for the system is obtained. The proposed functional can take full advantage of the upper and lower bounds of interval time lags and the intermediate values between these two bounds. The new criterion is given in the form of a linear matrix inequality, which is easily verified by MATLAB. Numerical examples show that compared with the methods in the references, the results of this paper can get a larger upper bound of the allowed delay, which also verifies the effectiveness of the method.