New methods are developed for the stabilization of a linear system with general time-varying distributed delays existing at the system’s states, inputs and outputs. In contrast to most existing literature where the function of time-varying delay is continuous and bounded, we assume it to be bounded and measurable. Furthermore, the distributed delay kernels can be any square-integrable function over a bounded interval, where the kernels are handled directly by using a decomposition scenario without using approximations. By constructing a Krasovskiĭ functional via the application of a novel integral inequality, sufficient conditions for the existence of a dissipative state feedback controller are derived in terms of matrix inequalities without utilizing the existing reciprocally convex combination lemmas. The proposed synthesis (stability) conditions, which take dissipativity into account, can be either solved directly by a standard numerical solver of semidefinite programming if they are convex, or reshaped into linear matrix inequalities, or solved via a proposed iterative algorithm. To the best of our knowledge, no existing methods can handle the synthesis problem investigated in this paper. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed methodologies.

开发了用于稳定线性系统的新方法，该线性系统具有在系统状态，输入和输出处存在的一般时变分布式延迟。与大多数时变延迟函数是连续且有界的文献相反，我们认为它是有界且可测量的。此外，分布式延迟内核可以是有界区间上的任何平方可积函数，其中可以通过使用分解方案而不使用近似值来直接处理内核。通过应用一个新的积分不等式构造一个Krasovskiĭ泛函，就可以根据矩阵不等式推导存在耗散状态反馈控制器的充分条件，而无需利用现有的双向凸组合引理。拟议的综合（稳定性）条件（考虑了耗散性）可以通过半定规划的标准数值求解器（如果是凸的）直接求解，也可以重整为线性矩阵不等式，或者通过拟议的迭代算法求解。据我们所知，没有任何现有方法可以解决本文研究的综合问题。最后，通过数值例子说明了所提出方法的有效性。