Componentwise bounds and invariant sets for switched systems with nonlinear delayed-state-dependent perturbations

We present a novel method to compute componentwise transient bounds, componentwise ultimate bounds, and invariant regions for switched continuous-time linear systems with perturbation bounds that may depend nonlinearly on a delayed state. The main advantage of the method is its componentwise nature, i.e. the fact that it allows each component of the perturbation vector to have an independent bound and that the bounds and sets obtained are also given componentwise. This componentwise method does not employ a norm for bounding either the perturbation or state vectors, and thus may avoid conservativeness due to different perturbation or state vector components having substantially different bounds. We give conditions for the derived bounds to be of local or semiglobal nature. In addition, we deal with the case of perturbation bounds that depend linearly on a delayed state as a particular case of the nonlinear dependence for which the bounds derived are shown to be globally valid. A novel sufficient condition for practical stability is also provided.