The following problems are solved for systems of differential equations with periodic or aperiodic impulses, when uncertain disturbances are taken into account: estimating the set of solutions with initial data from a given ellipsoid in the form of an evolving invariant ellipsoid; the synthesis problem of continuous-impulse control, providing finite time boundedness of the original system with respect to given sets. Using the quadratic Lyapunov function with variable parameters, these problems are reduced to optimization problems with differential and difference linear matrix inequalities. The results are illustrated by the second order example.

中文翻译：

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不确定扰动线性非周期脉冲系统的状态估计与控制

当考虑不确定扰动时，对于具有周期性或非周期性脉冲的微分方程系统，解决了以下问题： 用演化不变椭球形式的给定椭球的初始数据估计解集；连续脉冲控制的综合问题，提供原始系统关于给定集合的有限时间有界性。使用具有可变参数的二次李雅普诺夫函数，这些问题被简化为具有微分和差分线性矩阵不等式的优化问题。结果由二阶示例说明。