不确定线性离散时滞系统的指数稳定性

Exponential Stability for Uncertain Linear Discrete-Time Systems with Time-Varying Delays

采用属于超长方体的时变参数向量描述不确定性,利用仿射依赖于参数的Lyapunov泛函研究不确定线性离散时滞系统的指数稳定性问题,由Lyapunov泛函的指数衰减性保证系统的指数稳定性.引入仿射依赖于参数的自由权矩阵分析Lyapunov泛函的指数衰减性,利用多凸函数的性质把含时变参数的矩阵不等式转化成线性矩阵不等式,从而得到了指数稳定的充分条件.由于有效利用了不确定时变参数和其增量的上下界信息,并且采用凸组合方法处理区间时变时滞,因此所得方法具有较小的保守性.最后用数值算例验证了所得方法的有效性.

The uncertainties were described as time-varying parameter vectors belonging to a hyper rectangle. The problem of exponential stability for uncertain linear discrete-time systems with time-varying delays was investigated by using affine parameter-dependent Lyapunov functional. Exponential stability was guaranteed by the exponential decay of the Lyapunov functional. Affine parameter-dependent free-weighting matrices were introduced to analyze the exponential decay of the Lyapunov functional, and the matrix inequalities containing time-varying parameters were transferred to linear matrix inequalities by using the properties of multi-convex function. Therefore, a sufficient condition for exponential stability was obtained. Since the information of upper and lower bounds of the uncertain time-varying parameters and their increments was effectively used and the convex combination method was applied when handling interval time-varying delay, the proposed method had less conservatism. An example was presented to show the effectiveness of the proposed method.