In this paper, the problem of robust stability for linear time-varying implicit dynamic equations is generally studied. We consider the effect of uncertain structured perturbations on all coefficient matrices of equations. A formula of stability radius with respect to dynamic structured perturbations acting on the right-hand side coefficients is obtained. In case where structured perturbations affect on both derivative and the right-hand side, the lower bounds for the stability radius are derived. The results are novel and extend many previous results about robust stability for time-varying ordinary differential/difference equations, time-varying differential algebraic equations and time-varying implicit difference equations.

本文主要研究线性时变隐式动力方程的鲁棒稳定性问题。我们考虑了不确定的结构扰动对方程所有系数矩阵的影响。获得了关于作用在右侧系数上的动态结构化扰动的稳定半径的公式。如果结构性扰动同时影响导数和右侧，则导出稳定半径的下限。结果是新颖的，并扩展了许多关于时变常微分/差分方程，时变微分代数方程和时变隐式差分方程的鲁棒稳定性的先前结果。