Uniform ultimate boundedness of the solutions of uncertain dynamic delay systems with state-dependent and memoryless feedback control

A continuous feedback controller is developed for a class of non-linear, time-varying, uncertain systems governed by functional differential equations with retarded arguments. The form of the controller guarantees that under certain assumptions all solutions are uniformly bounded in norm for time t sufficiently largo in spite of the uncertainty in system parameters and input signals. Furthermore, given any ϵ > 0, the parameters in the description of the controller can be chosen such that the closed-loop solutions all satisfy ||x(t)|| ≤ ϵ for large t.