A practically significant effect of a surge occurrences in linear dynamical systems under nonzero initial conditions is explored. The linear dynamical system subjected to unknown-but-bounded exogenous disturbances is considered. Using the apparatus of linear matrix inequalities and the invariant ellipsoids concept, the estimations of the upper bounds of the trajectories deviations are obtained, and an approach is suggested to the feedback design that minimizes the deviations. The efficacy of the approach proposed is illustrated on numerical examples.

中文翻译：

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有界扰动的线性动力系统中偏差的上界

探索了在非零初始条件下线性动力系统中电涌发生的实际影响。考虑受到未知但有界外生干扰的线性动力学系统。利用线性矩阵不等式和不变椭球概念的装置，获得了轨迹偏差上限的估计，并提出了一种将偏差最小化的反馈设计方法。数值示例说明了所提出方法的有效性。