Fuzzy descriptor observer-based stabilization for nonlinear systems with measurement delays: Application to overhead crane liquid container systems

This paper investigates output-feedback control design in the presence of output measurement delays for the anti-sloshing problem of an overhead crane with a liquid container. A double-pendulum overhead crane (DPOC) is first adopted to describe the system dynamics, where the crane–liquid container system is modeled using a descriptor Takagi–Sugeno fuzzy (DTSF) framework. In contrast to existing feedback-control approaches for DPC, which typically assume that all system states are measurable and that output measurements are delay-free, this work addresses both issues simultaneously by developing an observer-based controller within an extended DTSF framework that explicitly accounts for output measurement delays. By constructing the observer directly in the DTSF representation, the proposed approach significantly reduces the number of fuzzy rules compared with methods based on full state–space transformations, while still preserving the inherent nonlinear characteristics of the system in the observer design. Furthermore, by extending the DTSF formulation to include output delays, sufficient stability conditions for the observer-based control system are derived using a quadratic Lyapunov function combined with the Halanay inequality. These conditions are expressed in terms of linear matrix inequalities (LMIs), making the controller synthesis computationally feasible via LMI problems. Finally, numerical simulations and comparative studies are conducted on both a rotary inverted pendulum and the DPOC system to demonstrate the effectiveness and robustness of the proposed method.