Functional observer for switched discrete-time singular systems with time delays and unknown inputs

This study considers the functional observers design for a class of discrete-time switched singular systems simultaneously subject to state delays, unknown inputs (UIs) and arbitrary switching sequences. The singular matrix E is assumed to be switching-mode-dependent, and the UIs are present in both the state and the measurement channels. A mode-dependent, delay-type observer is first constructed, then, based on the unknown input decoupling and the switched Lyapunov theory, a method is proposed to design such observer which ensures both: the total elimination of the UIs and exponential estimate of the given function of the state vector. The conditions for the existence of the proposed observer are given through algebraic matrix inequalities, and exponential stability of the observation error dynamics is derived by using a properly constructed decay-rate-dependent switched Lyapunov function and the linear matrix inequality technique. Finally, an illustrative example is given to show the effectiveness of the obtained results.