In this paper, the nonlinear robust $H_{\infty }$ control is investigated for nonlinear course control systems of unmanned surface vessel (USV) with uncertain parameters and external disturbance. Firstly, we suppose that the part or all of the system parameters are unknown but within some ranges, due to the effect of different conditions such as the loading of ship. Then, the course system is modeled as a polynomial one with time invariant polytopic uncertainty. With the aid of parameter dependent Lyapunov function method and positive polynomial theory, the sufficient conditions are given for stability and stabilization with $H_{\infty }$ 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. Finally, simulation results show the effectiveness of the approach.

Since the sideslip angle is often ignored or simplified in the process of path following of unmanned surface vehicle by using the line-of-sight (LOS) guidance law because of its fast change and the difficulty of measurement, an observer was proposed by internal model control (IMC) to quickly estimate the sideslip angle in the LOS guidance law. First, a prediction model was established for the tracking error, and a state space model for prediction errors was constructed as an internal model. With the introduction of the auxiliary variables, a new augmented system was set up for a state space model of the prediction errors. Then, the sideslip angle observer was designed by the theory of state feedback with the feature of the control law of a proportional-integral type. Theoretically, the stability of the system was proved based on the Lyapunov criteria. A simulation and experiment verified the effectiveness of the proposed sideslip angle observer in improving the path-following accuracy. The results show that the IMC-based observer introduces a proportional term of tracking error that is not considered by other observers, which is easier to implement and adjust, and has a faster response speed and a smaller steady-state error for the sideslip angle. In addition, the assumption of a small sideslip angle is not introduced in the design process, so the proposed observer provides an accurate estimation method for a large sideslip angle.

This paper focuses on the robust mean-square consensus control problem for linear multiagent systems over randomly switching signed interaction topologies. The stochastic process is governed by a time-homogeneous Markov chain with partly unknown transition rates. Sufficient conditions for a consensus in the form of linear matrix inequalities are given via distributed adaptive control based on parameter-dependent Lyapunov functions. The adaptive control protocols require only the neighbor information of the agents, and the algorithm that designs the protocols reduces the influence of the communication topology on the consensus, which can prevent undesirable interaction impacts. Moreover, the disturbance rejection problem is addressed as an extension. Finally, two simulations are utilized to illustrate the effectiveness of the algorithms.