时滞连续正系统的性能分析与控制器设计

Performance analysis and controller design for positive systems with time delay

在现实世界中,存在一类实际系统,其相应的动力学系统可以用正系统来刻画。这类系统在交通流量控制,电力系统,系统生物学,经济学模型和化学工业等领域有着广泛的应用,因而近年来不断得到越来越多的来自不同学科研究学者的兴趣。本文研究的是用线性规划的形式表示时滞正系统稳定的充分、必要条件以及时滞正系统L_1诱导性能指标的刻化条件。在此基础上,推导出鲁棒静态输出反馈控制器的存在条件,并建立迭代优化方法来求解控制器存在的条件。最后,本文用一个实例来验证该理论方法的可行性和有效性。

In real world,there are many practical systems whose corresponding dynamical systems can be described by the positive system. This kind of system can be found in traffic control, power system, biological system, economic model and chemical industry and so on has a widely used and in recent years. Positive systems continue to attract more and more interest from researchers in different disciplines. This paper is concerned with theL1 -induced performance analysis for continuous-time positive systems with time delay. A necessary and sufficient condition for stability andLl- induced performance of positive linear systems is proposed in terms of linear ine- qualities. Based on this, conditions for the existence of robust static output-feedback controllers are established and an iterative convex op- timization approach is developed to solve the conditions. An illustrative example is provided to show the effectiveness and applicability of the theoretical results.