Incremental Passivity and Incremental Passivity-Based Output Regulation for Switched Discrete-Time Systems

This paper investigates incremental passivity and output regulation for switched discrete-time systems. We develop the results in two parts. First of all, a concept of incremental passivity is proposed to describe the overall incremental passivity property of a switched discrete-time system in the absence of the classic incremental passivity property of the subsystems. A condition for incremental passivity is given. A certain negative output feedback is designed to produce asymptotic stability. Incremental passivity is shown to be preserved under feedback interconnection. The second part of this paper is concerned with an application of the incremental passivity theory to the output regulation problem for switched discrete-time systems. The key idea is to construct a switched internal model with incremental passivity, which closely links the solvability of the output regulation problem. A characteristic of the switched internal model is that it does not necessarily switch synchronously with the controlled plant, which greatly increases the freedom of design. Once such a switched internal model is established, the output regulation problem is then solved by construction of the feedback interconnection between the controlled plant and the switched internal model. The main usefulness of the strategy is to get rid of the solvability of the output regulation problem for the subsystems.