This paper is concerned with exponential quasi-dissipativity for switched nonlinear systems using multiple storage functions and multiple supply rates. First, a new concept of exponential quasi-dissipativity for a switched nonlinear system is proposed. In contrast with dissipative system which does not produce energy in some abstract sense, the supply rate of quasi-dissipativity is the sum of the conventional dissipativity supply rate and the constant supply rate. This means quasi-dissipative system can produce energy by itself. Each active subsystem is only required to be exponentially quasi-dissipative, while the energy changing of each inactive subsystem characterized by cross-supply rates is considered as the transformation of “energy” from the active subsystem. By weakening the conventional dissipation inequality, a broader class of open-loop systems and controllers are admissible, leading to broader application. Second, the ultimate boundedness property is obtained under some constraints on the energy changing of inactive subsystems. Third, the exponential quasi-dissipativity conditions for switched nonlinear systems are obtained by the design of a state-dependent switching law. In particular, the sufficient conditions of exponential quasi-passivity and exponential finite power gain for switched nonlinear systems are given thereby providing generalizations of KYP conditions and HJI inequality. Finally, the effectiveness of the obtained results is verified by two examples.

本文涉及使用多个存储函数和多个电源速率的开关非线性系统的指数拟耗散性。首先，提出了一种非线性切换系统的指数准耗散性的新概念。与在某种意义上不产生能量的耗散系统相反，准耗散性的供给率是常规耗散性供给率和恒定供给率之和。这意味着准耗散系统可以自行产生能量。每个活动子系统仅要求是指数准耗散的，而每个以交叉供电速率为特征的非活动子系统的能量变化被视为活动子系统的“能量”转换。通过削弱传统的耗散不等式，允许使用更多种类的开环系统和控制器，从而导致更广泛的应用。其次，在对非活动子系统的能量变化施加一定约束的情况下获得了最终有界性。第三，通过设计与状态有关的开关定律，获得了非线性开关系统的准拟耗散条件。特别地，给出了切换非线性系统的指数拟无源性和指数有限功率增益的充分条件，从而提供了KYP条件和HJI不等式的概括。最后，通过两个例子验证了所获得结果的有效性。最终有界性是在非活动子系统能量变化的某些约束条件下获得的。第三，通过设计与状态有关的开关定律，获得了非线性开关系统的准拟耗散条件。特别地，给出了切换非线性系统的指数拟无源性和指数有限功率增益的充分条件，从而提供了KYP条件和HJI不等式的概括。最后，通过两个例子验证了所获得结果的有效性。最终有界性是在非活动子系统能量变化的某些约束条件下获得的。第三，通过设计与状态有关的开关定律，获得了非线性开关系统的准拟耗散条件。特别地，给出了切换非线性系统的指数拟无源性和指数有限功率增益的充分条件，从而提供了KYP条件和HJI不等式的概括。最后，通过两个例子验证了所获得结果的有效性。给出了切换非线性系统的指数拟无源性和指数有限功率增益的充分条件，从而提供了KYP条件和HJI不等式的概括。最后，通过两个例子验证了所获得结果的有效性。给出了切换非线性系统的指数拟无源性和指数有限功率增益的充分条件，从而提供了KYP条件和HJI不等式的概括。最后，通过两个例子验证了所获得结果的有效性。