Passivity and Stability of Switched Systems Under Quantization

Passivity theory is a well-established tool for analysis and synthesis of dynamical systems. Recently, this work has been extended to switched and hybrid systems where passivity and stability results of single systems as well as interconnected systems are derived. However, the results may no longer hold when quantization is present as is the case with digital controllers or communication channels. The contribution in this paper is to introduce a control framework under which passivity for switched and non-switched systems can be maintained. This framework centers on the use of an input-output coordinate transformation to recover the passivity property. In order to present these results, background material is provided on passive quantization and output strict passivity for switched and non-switched systems. The proposed framework is first presented for non-switched systems and then generalized to switched systems.