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

Abstract This article makes some efforts towards discussing the problem of observer design for a kind of discrete-time T-S fuzzy singular systems corrupted by process disturbances and measurement noises. To situate our design scheme in a more practical context, the premise variables of fuzzy systems under consideration are unmeasurable, and the process disturbances are only partially decoupled rather than completely decoupled. By integrating the fuzzy Lyapunov function method and the linear matrix inequality technique, an unknown input observer which can not only decouple partial process disturbances, but also attenuate the influence of measurement noises and non-decoupled process disturbances is proposed to achieve state reconstruction. Particularly, to reduce the conservatism, some slack matrices and scalars are utilized in observer design to obtain extra degrees of freedom. Finally, the performance of theoretical results is fully verified via two numerical simulations.