Stabilization of Uncertain Feedforward Nonlinear Systems With Application to Underactuated Systems

This note presents saturated controllers to stabilize uncertain feedforward nonlinear systems whose nominal dynamics contains uncertain “gains” and is subject to linear perturbations. We assign a class of saturated controllers within which multiplicative coefficients appear before both states and saturation functions, and the convergence analysis is conducted in the following way: to verify the reduction of saturated terms, we calculate the time derivative of a boundary surface in a small domain when the states reach the boundary surface; to prove the asymptotic stability of the corresponding reduced system, we use an M-matrix-based comparison principle. In this way, the suggested algorithm does not depend on the small-gain theory, and is suitable for dealing with strongly nonlinear underactuated systems including the cart-pendulum system, the overhead crane system, and the uncertain vertical takeoff and landing vehicle.