This paper studies geometrical quasi-dissipativity and boundedness properties for switched discrete-time nonlinear systems. First, a new concept of geometrical quasi-dissipativity for a switched discrete-time nonlinear system is proposed. In contrast with geometrically dissipative system, the supply rate of geometrical quasi-dissipativity is the sum of the conventional dissipativity supply rate and the constant supply rate, which means geometrically quasi-dissipative system can produce energy by itself. Then, a geometrically quasi-dissipative switched nonlinear system is shown to be uniformly ultimately bounded under some restricted conditions on the energy changing of inactive subsystems. Second, the sufficient conditions to be geometrical quasi-dissipative are obtained by the design of a more general state-dependent switching law. Third, a composite state-dependent switching law is designed to render interconnected switched systems geometrically quasi-(Q,S,R)-dissipative. The designed switching law allow the interconnected switched nonlinear systems to switch asynchronously. Finally, the effectiveness of the obtained results is verified by an example of a thermal system.

本文研究了切换离散时间非线性系统的几何准耗散性和有界性质。首先，提出了开关离散时间非线性系统的几何准耗散性的新概念。与几何耗散系统相比，几何准耗散系统的供给速率是常规耗散供给速率和恒定供给速率之和，这意味着几何准耗散系统可以自行产生能量。然后，在非活动子系统能量变化的某些限制条件下，几何准耗散切换非线性系统被证明是一致最终有界的。其次，几何准耗散的充分条件是通过设计更一般的状态相关开关定律来获得的。第三，复合状态相关开关定律旨在使互连的开关系统在几何上呈准（Q，S，R）耗散。设计的切换律允许互连的切换非线性系统异步切换。最后通过一个热力系统​​实例验证了所得结果的有效性。