Adaptive robust control of uncertain nonlinear systems with nonlinear delayed state perturbations

The problem of robust stabilization of uncertain nonlinear dynamical systems with multiple time delays is considered. In the paper, the upper bound of the nonlinearity and uncertainty, including delayed states, is assumed to be a linear function of some parameters which are still assumed to be unknown. Here, we do not require that the nonlinear terms including delayed states are linear norm-bounded in the states. An improved adaptation law with σ -modification is employed to estimate the unknown parameters, and a class of memoryless adaptive robust state feedback controllers is proposed. It is also shown that the proposed adaptive robust controllers can guarantee the uniform asymptotic stability of uncertain nonlinear time-delay systems. Finally, as a numerical example, an uncertain time-delay ecosystem with two competing species is given to demonstrate the validity of the results.