A constructive condition for inaccessible signal rejection with quadratic stability in discrete-time linear switching systems

This work deals with rejection of inaccessible signals in discrete-time linear switching systems, with the requirement that the compensated system be quadratically stable under arbitrary switching. A constructive condition is provided for devising a switching state feedback achieving zero output for any admissible inaccessible input sequence and any initial state in a certain subspace, while attaining quadratic stability under arbitrary switching of the closed-loop dynamics. The constructive condition is twofold, since structural and stability issues are considered independently of each others. The methodological bases consist of both classic and novel ideas of the geometric approach, enhanced with the notion of quadratic stability under arbitrary switching. The theoretical results are supported by a complete computational framework, developed in Matlab by using the algorithms of the geometric approach and the LMI solvers.