Geometrical quasi-dissipativity and boundedness property for switched discrete-time nonlinear systems

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.