A straightforward approach to state predictive control for continuous-time systems with nonuniform input delays

This paper revisits the control law derived with the backstepping approach through delay compensation for systems with distinct nonuniform input delays. As one of the main topics of the present paper, an interpretation of its control philosophy is provided through a very elementary viewpoint for better understanding and explanation of the control law. The course of such an interpretation, however, is associated with the use of some ‘implicit idealizing assumptions,’ and with regards to their use, the arguments are further extended to an elementary proof for the finite spectrum assignment property of the closed-loop system. It immediately implies the stability of the closed-loop system, but the arguments in the present paper are carried out through the treatment of the characteristic equation in the frequency-domain, and thus are in stark contrast with the time-domain stability proof with the Lyapunov functional used in the existing studies in which the control law was derived. In addition, the case when the state of the delay-free part of the system is not accessible and a state observer is introduced for it is further studied, and the combined use of the state-feedback-based control law and the state observer is studied. Through a simple modification of the frequency-domain proof for the closed-loop stability in the state feedback case, the separation principle in such a context is further established. A numerical example is also studied to confirm the robustness of the closed-loop system under the plant uncertainties including the mismatch in the input delays.