Abstract
Looped-functionals have been shown to be relevant for the analysis of a wide variety of systems. However, the conditions obtained in previous papers on the analysis of sampled-data, impulsive and switched systems have only been shown to be sufficient for the characterisation of their associated discrete-time stability conditions. We prove here that these conditions are also necessary. This result is derived for a wider class of linear systems, referred to as impulsive pseudo-periodic systems, that encompass periodic, impulsive, sampled-data and switched systems as special cases.
Notes
1. Note that this sequence does not admit any accumulation point and is unbounded from above.
2. The state is assumed to be right-continuous and the left-limit at tk is denoted by x(t−k) = lims↑0x(tk + s).