Bounding the distance to the nearest unobservable switched linear time-invariant system

This paper presents algorithms for computing lower and upper bounds on the distance to the nearest unobservable switched linear time-invariant (SLTI) system. In particular a SLTI system subject to real perturbations, an unknown switching sequence, unknown initial state, and no continuous control input is examined. The perturbations considered are additive real structured perturbations to the A- and C- state model matrices of each mode. The lower and upper bounds are constructed by considering larger and smaller sets of allowable real perturbations, respectively.