Stability equivalence between regime‐switching jump diffusion delayed systems and corresponding systems with piecewise continuous arguments and application to discrete‐time feedback control

Abstract

AbstractIn this paper, we mainly study the equivalence of exponential stability for regime‐switching jump diffusion delayed systems (RSJDDSs) and RSJDDSs with piecewise continuous arguments (RSJDDSs‐PCA). Our results show that if one of the RSJDDS and the RSJDDS‐PCA is th moment exponentially stable, then another system is also th moment exponentially stable when time delay and segment step size have a common upper bound, while both equations are almost surely exponentially stable, and we also provided a method to calculate this upper bound. In addition, as an application of the stability equivalence theorem, we design discrete‐time state and mode observations feedback control to stabilize unstable RSJDDSs and investigate that controllers of the drift, diffusion, and jump terms are all able to play a stabilizing effect on the controlled system.