Almost dissipativity and ultimate boundedness property for switched nonlinear systems

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.