A nonlinear state feedback design for nonlinear systems with input delay

This paper is devoted to the design of a nonlinear feedback law based on state prediction for nonlinear systems with input time-delay. We successively consider the case of known constant time-delay and the case of time-varying delay in the input. In the case of constant delays and as in the linear case (under the finite-spectrum assignment assumption), a nonlinear distributed-delay control law is obtained. Since the computation of delay-distributed control laws remain a difficult problem as in the linear case, we discuss a control law approximation which is derived by using both a state prediction approximation and the “dynamic inversion” of a fixed point problem. In the case of time-varying delays, we extend the approach proposed in [9] by using a control law similar to the linear case one, together with dynamic inversion of a fixed point problem. Finally two illustrative examples are provided that demonstrate the effectiveness of the approach.