On the input-to-state practical stabilization of nonlinear neutral systems

This paper deals with the input-to-state practical stabilization of nonlinear systems described by neutral functional differential equations in Hale´s form, affine in the control input. An unknown, Lebesgue measurable, locally essentially bounded disturbance adding to the control law, which describes actuator and general control design errors, is considered. The Arstein-Sontag approach, integrated with the Sontag´s input-to-state stability redesign method, is followed. Sufficient conditions in terms of the existence of a suitable invariantly differentiable control Lyapunov-Krasovskii functional, which allow the construction of an input-to-state practically stabilizing controller, are provided. If the disturbance is bounded, the projected controller yields the system state to approach asymptotically an arbitrarily small neighborhood of the origin, by increasing the value of a control tuning parameter.