Design of stabilizing controllers for high order feedforward nonlinear systems with delayed input

This paper investigates the problem of global robust stabilization by state feedback, for a family of high order feedforward (upper-triangular) nonlinear systems with delayed input. The uncertain nonlinearities are assumed to satisfy a polynomial growth assumption with a constant growth rate. The designed controllers, which are continuous but not smooth feedbacks, could achieve global asymptotical stability. Based on the appropriate state transformation of time-delay systems, the problem of controller design can be converted into the problem of finding a parameter, which can be gotten by appraising the nonlinear terms of the systems. An example is given to show the effectiveness of the proposed design procedure.