Robust observer design for T-S fuzzy singular systems with unmeasurable premise variables and partially decoupled disturbances

Robust observer design plays a key role in state-based feedback control and real-time fault estimation. Accordingly, an unknown input observer design scheme for a kind of discrete-time T-S fuzzy singular systems corrupted by process disturbances and measurement noises is explored in this article. Compared to some previous results, the premise variables of fuzzy systems under consideration are unmeasurable, and the process disturbances studied here are assumed to be only partially decoupled rather than completely decoupled. All these characteristics make our design in a more practical context. Then, a novel observer synthesis scheme which can not only decouple partial process disturbances, but also attenuate the influence of non-decoupled process disturbances and measurement noises is developed by utilizing the fuzzy Lyapunov function method, and observer parameters can be solved in terms of linear matrix inequalities. In particular, to reduce the conservatism, some slack matrices and scalars are introduced into the observer synthesis scheme, which are helpful for obtaining additional degrees of freedom. Finally, the performance of theoretical results is fully verified via two numerical simulations.