On stabilizing strict-feedback linear 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 dasiafeedforwardpsila form. We consider a specially selected example of an exponentially unstable system with simultaneous input and state delays, which contains some key features that make the standard matrix exponential based predictor feedback design inapplicable. We construct an explicit feedback law, which contains distributed delay feedback of the input and the delayed state, and present a Lyapunov stability analysis.