Stabilization of linear strict-feedback systems with delayed integrators

The problem of compensation of input delays for unstable linear systems was solved in the late 1970s. The systems with simultaneous input and state delay have remained a challenge, although exponential stabilization has been solved for systems that are not exponentially unstable, such as chains of delayed integrators and systems in the `feedforward´ form. We consider a general system in strict-feedback form with delayed integrators, which is an example of an exponentially unstable system with simultaneous input and state delays, and design a predictor feedback controller for this class of systems. Exponential stability is then proven using a Lyapunov-Krasovskii functional.