  A simultaneous mode, input and state set-valued observer is proposed for
hidden mode switched linear systems with bounded-norm noise and unknown input
signals. The observer consists of two constituents: (i) a bank of mode-matched
observers and (ii) a mode estimator. Each mode-matched observer recursively
outputs the mode-matched sets of compatible states and unknown inputs, while
the mode estimator eliminates incompatible modes, using a residual-based
criterion. Then, the estimated sets of states and unknown inputs are the union
of the mode-matched estimates over all compatible modes. Moreover, sufficient
conditions to guarantee the elimination of all false modes are provided and the
effectiveness of our approach is exhibited using an illustrative example.
