We deal with the reachability problem for linear and bilinear discrete-time uncertain systems under integral non-quadratic constraints on additive input terms and set-valued constraints on initial states. The bilinearity is caused by an interval type uncertainty in coefficients of the system. Algorithms for constructing external parallelepiped-valued (shorter, polyhedral) estimates of reachable sets are presented. For linear time-invariant systems, two techniques for constructing touching external estimates with constant orientation matrices are described and compared. For time-dependant bilinear systems, parallelepiped-valued estimates are constructed. For bilinear systems with constant coefficients, nonconvex estimates are proposed in the form of unions of parallelepipeds. Evolution of all estimates is determined by systems of recurrence relations.

中文翻译：

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具有可加项积分界的离散时间系统可达集的外部多面体估计

我们处理线性和双线性离散时间不确定系统在加性输入项的积分非二次约束和初始状态的设置值约束下的可达性问题。双线性是由系统系数的区间类型不确定性引起的。提出了用于构建可达集的外部平行六面体值（较短、多面体）估计的算法。对于线性时不变系统，描述并比较了两种用于构造具有恒定方向矩阵的接触外部估计的技术。对于瞬态双线性系统，构造平行六面体值估计。对于具有常数系数的双线性系统，非凸估计以平行六面体并集的形式提出。