Observer design for discrete T-S fuzzy time-delay singular systems

In this paper, we investigate the design of observers tailored for discrete T-S fuzzy time-delay singular systems, considering the presence of process disturbances and measurable premise variables. An observer with more design degrees of freedom than the commonly used Luenberger observer is designed. By constructing an asymmetric Lyapunov-Krasovskii functional, a criterion ensuring the existence of the fuzzy state observer is provided, which eliminates the limitations of the positive definiteness and symmetry of the previous functional matrix. In the process of solving the inequality, the relaxation matrix is incorporated to acquire additional flexibility and alleviate the conservatism of parameter design. Ultimately, two numerical instances are provided to thoroughly validate the rationale and efficacy of the approach.