Two state observers are designed for some classes of switched linear systems with unknown inputs. The design of the proposed observers assumes that all switching subsystems fulfill a property of "strong detectability" [4] that allows to implement suitable reduced-order unknown-input switched observers. The synthesis of the observers is based on the feasibility of a certain system of LMIs. Two main schemes are presented. For the case when the set of possible unknown-input distribution matrices are linearly dependent, an observer is suggested that guarantees the asymptotic state reconstruction without imposing any slow-switching dwell-time constraint about the sequence of the switching times. For the general case, the existence of a minimal average dwell-time for every switching sequence is assumed. By appropriate Lyapunov analysis, the convergence of the state estimate is proven to be exponential in both cases. Simulation results confirm the predicted performance.