Designing ship controllers is a challenging problem because of nonlinear dynamics, uncertainty in parameters and external disturbances. Furthermore, the interaction between yaw and roll angles increase the complexity of this issue when autopilot and roll stabilizer are considered together. In this research, a MIMO sliding mode controller is designed to control yaw and roll angles simultaneously. The major contribution of the paper is designing an integrated controller based on a nonlinear model of ship as well as considering analytic bounds of uncertainties. Then, in order to reduce the chattering phenomenon and to improve the tracking ability of the system, the control scheme has been modified using an integral switching variable. Simulation results show the success of the proposed method to overcome nonlinearity and disturbances, as well as high performance in rough wave conditions. Also, comparison between the proposed controller and two SISO control schemes demonstrates advantages of the integrated control method.

This paper deals with stability analysis of hybrid systems. Such systems are characterized by a combination of continuous dynamics and logic based switching between discrete modes. Lyapunov theory is a well known methodology for the stability analysis of linear and nonlinear systems in control system literature. Construction of Lyapunov functions for hybrid systems is generally a difficult task, but once these functions are defined, stabilization of the system is straight-forward. The sum of squares (SOS) decomposition and semidefinite programming has also provided an efficient methodology for analysis of nonlinear systems. The computational method used in this paper relies on the SOS decomposition of multivariate polynomials. By using SOS, we construct a (some) Lyapunov function(s) for the hybrid system. The reduction techniques provide numerical solution of large-scale instances; otherwise they will be practically unsolvable. The introduced method can be used for hybrid systems with linear or nonlinear vector fields. Some examples are given to demonstrate the capabilities of the proposed approach.