Uniform stability of switched linear systems with persistent dwell-time and bounded additive disturbance

In this paper, the stability problem for a class of discrete-time switched linear systems with bounded additive disturbance is investigated. The disturbance is assumed to be amplitude-bounded and the switching signal is considered to be persistent dwell-time (PDT) switching. The global uniform stability criterion (GUAS) for the nominal switched systems with PDT switching is first established, then a PDT robust positive invariant (RPI) set is determined allowing for the bounded additive disturbance. Based on the PDT RPI set, a concept of generalized robust positive invariant (GRPI) set under PDT switching is further proposed, and it is demonstrated that the disturbed system is also asymptotically stable in the sense of converging to the PDT GRPI set. A numerical example is provided to verify the theoretical findings.