The Output Regulation Problem with Stability for Linear Switching Systems: A Geometric Approach

This work provides a solution for the output regulation problem with quadratic stability under arbitrary switching in linear switching systems. Extension to other stability requirements, like, e.g., asymptotic stability, is also considered, and it is shown to have a limited, although sharp, impact on the proposed solution. The main reason is that the geometric approach, which is at the basis of the developed methodology, allows the structural aspects of the problem to be considered separately from the stability aspects. For the same reason, continuous-time systems and discrete-time systems are given a unified treatment as far as the structural issues are concerned, while different technicalities characterize the presentation of the stability issues.