Backstepping designs in the presence of non-constant delays on the virtual input

Abstract

We present results on stabilization of nonlinear systems in the strict-feedback form with delays affecting the virtual inputs. We consider systems with constant and time-varying delays, as well as systems with delays that depend on the current or past states, which arise in numerous applications, such as, for example, in cooling systems. The design methodology is based on the concepts of infinite-dimensional backstepping and nonlinear predictor feedback. Several illustrative examples are provided.