On the interplay between periodic switches and uncontrolled jumps in linear discrete-time systems

This paper deals with the analysis of stability and the characterization of input-output norms for dual switching linear systems in discrete-time. These systems are subject to two independent switching signals, taking values in finite sets, coming from different sources. The first switching signal is periodic while the second is uncontrolled and generate parameter jumps which are either completely arbitrary or satisfy a prescribed dwell-time constraint. The overall system is a linear time-varying system exhibiting a complex dynamic behavior due to the interplay between the periodic switches and the uncontrolled jumps. LMI conditions for stability and guaranteed H
₂
norm input/output performances are provided. The results are obtained by merging the theory of linear periodic systems with recent developments on switched linear time-invariant systems.