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 modematched observers and (ii) a mode estimator. Each modematched 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.
A fixed-order set-valued observer is presented for linear parameter-varying systems with bounded-norm noise and under completely unknown attack signals, which simultaneously finds bounded sets of states and unknown inputs that include the true state and inputs. The proposed observer can be designed using semidefinite programming with LMI constraints and is optimal in the minimum H∞-norm sense. We show that the strong detectability of each constituent linear time-invariant system is a necessary condition for the existence of such an observer, as well as the boundedness of set-valued estimates. Furthermore, sufficient conditions are provided for the upper bounds of the estimation errors to converge to steady state values and finally, the results of such a set-valued observer are exhibited through an illustrative example.
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