Geometrical Quasi-Passivity and Practical Stability Property for Switched Discrete-Time Nonlinear Systems

This paper investigates geometrical quasi-passivity, feedback quasi-passification and related properties for switched discrete-time nonlinear systems using multiple storage functions and multiple supply rates. First, a concept of geometrical quasi-passivity for a switched discrete-time nonlinear system is firstly proposed to describe the overall quasi-passivity property of switched discrete-time nonlinear systems in the absence of the conventional geometrical quasi-passivity property of each active subsystem. Then, a geometrically quasi-passive switched nonlinear system is shown to be practically stable. Compared with passive switched system, quasi-passive switched system whose subsystems contain energy source can produce energy itself. Second, a state-dependent switching law is designed to achieve geometrical quasi-passivity. Finally, the feedback geometrical quasi-passification problem is solved by the design of a state-dependent switching law and a set of feedback controllers. A numerical example is presented to the effectiveness of the obtained results.