Adaptive Robust Stabilization of Cascaded Nonlinear Systems with Uncertain Time-Delay

Abstract

This paper is concerned with adaptive robust stabilization problem for a class of cascaded nonlinear systems with uncertain time-delay and unknown parameters. The cascaded system consists of two subsystems which are ξ-subsystem driven by the control input and x-subsystem forced by the output y of the ξ-subsystem. First, an extension of LaSalle-Yoshizawa theorem is given for the nonlinear time-delay systems, which provides a sufficient condition for convergence to zero of partial states with boundedness of the system. And then, it is shown that an adaptive robust stabilizing controller can be designed by this theorem, if the nominalξ-subsystem can be rendered strictly passive and the unforced x-subsystem is asymptotically stable. It is also shown that the proposed design method can be extended to the case where the ξ-subsystem has a triangular structure. A numerical example is given to demonstrate the effectiveness of the proposed method.