论文标题
混合鲁棒性：使用线性系统的示例对具有不确定确定性和随机参数的系统分析
Mixed robustness: Analysis of systems with uncertain deterministic and random parameters using the example of linear systems
论文作者
论文摘要
考虑了具有恒定系数的线性系统的鲁棒性。存在用于分析具有随机或确定性不确定性系统稳定性的方法和工具。同时，没有方法可以分析包含两种类型的参数不确定性的系统。回顾了鲁棒性的类型，并引入了新型的“混合参数鲁棒性”。它包括几种变体。所提出的混合鲁棒性问题的表述可以视为鲁棒性的经典确定性和概率方法之间的中间类型。列出了几种案例，其中易于解决任务。通常，使用方案方法对稳健系统的稳定性测试是适用的，但是这些测试在计算上可能很复杂。为了计算所需的稳定性概率，提出了一种基于强大D分区的简单图形方法。此方法适用于少量随机参数的情况。稳定概率的最终估计是以确定的方式计算的，可以任意精确地找到。描述了解决分配任务的近似方法。给出了对其他类型系统的混合鲁棒性的示例和概括。
Robustness of linear systems with constant coefficients is considered. There exist methods and tools for analyzing the stability of systems with random or deterministic uncertainties. At the same time, there are no approaches for the analysis of systems containing both types of parametric uncertainty. The types of robustness are reviewed and new type of "mixed parametric robustness" is introduced. It includes several variations. The proposed formulations of mixed robustness problems can be considered as intermediate type between the classical deterministic and probabilistic approaches to robustness. Several cases are listed in which the tasks are easily solved. In general, tests of the stability of robust systems using the scenario approach are applicable, but these tests can be computationally complex. To calculate the desired stability probability, a simple graphical approach based on a robust D-partition is proposed. This method is suitable for the case of a small number of random parameters. The final estimate of the probability of stability is calculated in a deterministic way and can be found with arbitrary precision. Approximate ways of solving the assigned tasks are described. Examples and generalization of mixed robustness to other types of systems are given.
