Nonlinear Robust H∞ Control For Ship Course Control System With Time-varying Uncertain Parameters

摘要

In this article, the nonlinear robust $mathrm{H}infty$ control is investigated for ship course control system with time-varying uncertain parameters and external disturbance. Firstly, we suppose that both the parameters and its derivatives of system are unknown but within some ranges, due to the effect of different conditions such as the speed, loading of ship. Sequently, the ship course system is modeled as a polynomial one with time variant polytopic uncertainties. With the aid of parameter dependent Lyapunov function method and positive polynomial theory, the sufficient conditions are given for stability and stabilization with $mathrm{H}infty$ performance. These conditions are formulated in terms of parameter-dependent nonlinear matrix inequalities which can be verified by semidefinite programming relaxations based on the sum of squares technique(SOS). Finally, simulation results show the effectiveness of the approach.