A theorem for UGAS and ULES of (passive) nonautonomous systems: Robust control of mechanical systems and ships (Q2710026)

The authors prove a theorem which states sufficient conditions for uniform global asymptotic stability and uniform local exponential stability for a class of nonlinear nonautonomous systems by means of the direct Lyapunov method in a form which is common in nonlinear adaptive control. The applications are referred to ship control systems with integral action. The integral action is needed in order to compensate constant or slowly-varying environment disturbances due to ocean currents, second-order wave-induced drift forces and wind forces. The authors consider a nonlinear control system for high-speed ships. The nonlinear control system takes into account nonlinear damping, Coriolis and centripetal forces, and uses properties like the symmetry of the inertia matrix, dissipative damping and the skew-symmetry of the Coriolis and the centripetal matrices.