In this assay, we investigate the problem of Autonomous Underwater Vehicle (AUV) robust stabilisation including time-varying delay, time-variable uncertainty in modeling, and input amplitude constraint of actuators. Due to system singularity, the main aim is not only stabilisation but also include regularity, and impulse free response for the closed loop system. Encountering methods to model uncertainty, saturation constraint and time-delay are norm bounded method, polytopic method, and delay-dependent criteria respectively. Here a new theorem is introduced and then is proved for the close loop stabilisation through Bilinear Matrix Inequality (BMI). We compare the superiority of this technique by some significant literature via simulation examples from conservativism aspect. Method scope includes both retarded and neutral time-delay systems with multiple delays in states. In continue, for the first time against of conventional state space model methods, we obtain a new descriptor model of an AUV and investigate its robust stability in different conditions based on presented theorem.

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