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A simultaneous mode, input and state set-valued observer is proposed forhidden mode switched linear systems with bounded-norm noise and unknown inputsignals. The observer consists of two constituents: (i) a bank of mode-matchedobservers and (ii) a mode estimator. Each mode-matched observer recursivelyoutputs the mode-matched sets of compatible states and unknown inputs, whilethe mode estimator eliminates incompatible modes, using a residual-basedcriterion. Then, the estimated sets of states and unknown inputs are the unionof the mode-matched estimates over all compatible modes. Moreover, sufficientconditions to guarantee the elimination of all false modes are provided and theeffectiveness of our approach is exhibited using an illustrative example.

Simultaneous Mode, Input and State Set-Valued Observers with Applications to Resilient Estimation Against Sparse Attacks