Observers design for switched discrete-time singular time-delay systems with unknown inputs

This paper addresses the state estimation problem for a class of switched discrete-time singular systems simultaneously subject to state delays, unknown inputs (UIs) and arbitrary switching sequences. A mode-dependent observer is constructed, and, in view of the observation performance and the realizability, two class of design methods are proposed. The first class is based on the principle of exact decoupling, which allows the observer to perfectly reconstruct the system state regardless the presence of UIs under stringent rank conditions. The second one, with the aid of introducing L2L2-attenuation of UIs to the state estimation error, relaxes the rank constraints required in the first class method while permitting the observer to give an unknown input approximately decoupled state estimation. In both methods, by defining an appropriate switched Lyapunov function and using the linear matrix inequality technique, sufficient conditions for the existence of the observer are given, and the convergence rate of the state estimation error is proved to be exponential. Finally, two numerical examples are given to show the effectiveness of the developed theoretical results.