A closed loop stability condition of switched systems applied to NCSs with packet loss

摘要

This paper derives stability criteria for a closed loop system where the open loop switches between linear subsystems over time. This result is applied to a NCS where packets may get lost (’dropout’), and where a model is used to fill in these missing parts in the feedback signal. Even in case of an unstable open loop system, conditions are derived for the closed-loop system to be stable. The technical result reduces the problem to an eigenvalue inclusion problem for a set of block-structured matrices, instead of invoking Lyapunov or passivity theory. The stability condition comes in two flavors, each of which can be useful as illustrated in a numerical example.