ABSTRACT

This paper establishes almost dissipativity theory for switched nonlinear systems. First, an almost dissipativity of switched nonlinear systems is defined using multiple storage functions and multiple supply rates. This dissipativity property means that each active subsystem is dissipative except for a ball. And the energy of the inactive subsystem is seen as the transformation from the active subsystem. By weakening the conventional dissipativity, a more extensive class of open-loop systems and controllers can be obtained, leading to broader application. Second, the ultimate boundedness is achieved by almost dissipativity under some restrictive conditions on the energy changing of inactive subsystems. Third, the almost dissipativity conditions for these systems are given. Based on these conditions, two types of switching laws are obtained to achieve almost dissipativity. Finally, the effectiveness of the proposed method is verified by a practical example a mass-spring-damping system.

摘要

本文建立了切换非线性系统的几乎耗散理论。首先，开关非线性系统的几乎耗散性是使用多个存储函数和多个供电速率来定义的。这种耗散特性意味着每个活动子系统都是耗散的，除了一个球。而非活动子系统的能量被看作是活动子系统的转换。通过削弱传统的耗散，可以获得更广泛的开环系统和控制器，从而获得更广泛的应用。其次，在非活动子系统能量变化的某些限制条件下，通过几乎耗散来实现最终有界。第三，给出了这些系统的几乎耗散条件。基于这些条件，获得了两种类型的开关定律以实现几乎耗散。最后，通过一个质量-弹簧-阻尼系统的实例验证了所提方法的有效性。