Basic Predictor Feedback for Single-Input Systems

Abstract

This chapter discusses the basic idea of a partial differential equation (PDE) backstepping approach for single-input LTI ordinary differential equation (ODE) systems with discrete input delay. The key point of the backstepping approach lies in it providing a systematic construction of an infinite-dimensional transformation of the actuator state, which yields a cascade system of transformed stable actuator dynamics and stabilized plant dynamics. The cascade system consisting of such infinite-dimensional stable actuator dynamics and finite-dimensional stabilized plant dynamics is referred to as the closed-loop “target system.” The chapter first presents an alternative view of the backstepping transformation based purely on standard ODE delay notation. Then the backstepping transformation is described in PDE and rescaled unity-interval transport PDE notation.