Delay-adaptive control for linear systems with distributed input delays

Abstract A majority of existing literature on adaptive method of time-delay systems concentrate on uncertainty in plant parameters or discrete input delays. This paper proposes a systematic adaptive control approach to solve stabilization problems of linear systems with unknown distributed input delays. Under the rescaled unity-interval notation, the uncertain delay leads the input vector to consist of unknown functions and unknown parameters as well. To resolve the coexistent uncertainties in delay and input vector, a reduction-based change of variable and a backstepping–forwarding transformation of the finite-dimensional plant state and the infinite-dimensional actuator state are introduced. Making use of these conversions, the certainty-equivalence-based control law and the Lyapunov-based update law are developed for adaptive stabilization.