On the necessity of looped-functionals arising in the analysis of pseudo-periodic, sampled-data and hybrid systems

We prove that the looped-functional considered in [1,2,3] for the analysis of sampled-data, impulsive and switched systems is “complete”, in the sense that it can be used to equivalently characterize a certain discrete-time stability criterion involving matrix exponentials. This result is derived for a wider class of linear systems, referred to as pseudo-periodic systems with impulses, encompassing periodic, impulsive, sampled-data and switched systems.