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In this paper, the problem of exponential stability analysis and the design of sampled-data nonlinear systems have been studied using a polytopic linear parameter-varying approach. By means of modeling a new double-layer polytopic formulation for nonlinear sampled-data systems, a modified form of piecewise continuous Lyapunov-Krasovskii functional is proposed. This approach provides less conservative robust exponential stability conditions by using Wirtinger's inequality in terms of linear matrix inequalities. The distances between the real continuous parameters of the plant and the measured parameters of the controller are modeled by convex sets, and the analysis/design conditions are given at the vertices of some hyper-rectangles. In order to get tractable linear matrix inequality conditions for the stabilization problem, we performed relaxation by introducing a slack variable matrix. Under the new stability criteria, an approach is introduced to synthesize a sampled-data polytopic linear parameter-varying controller considering some constraints on the location of the closed-loop poles in the presence of uncertainties on the varying parameters. It is shown that the proposed controller guarantees the exponential stability of the closed-loop system for aperiodic sampling periods smaller than a known value, ie, maximum allowable sampling period. Finally, the effectiveness of the proposed approach is verified and compared with some state-of-the-art existing approaches through numerical simulations.

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This study has presented an efficient adaptive unscented Kalman filter (AUKF) with the new measurement model for the strapdown inertial navigation system (SINS) to improve the initial alignment under the marine mooring conditions. Conventional methods of the accurate alignment in the ship’s SINS usually fail to succeed within an acceptable period of time due to the components of external perturbations caused by the movement of sea waves and wind waves. To speed up convergence, AUKF takes into account the impact of the dynamic acceleration on the filter and its gain adaptively tuned by considering the dynamic scale sensed by accelerometers. This approach considerably improved the corrections of the current residual error on the SINS and decreased the influence due to the external perturbations caused by the ship’s movement. Initial alignment algorithm based on AUKF is designed for large misalignment angles and verified by experimental data. The experimental test results show that the proposed algorithm enhanced the convergence speed of SINS initial alignment compared with some state-of-the-art existing approaches.