State and delay reconstruction for nonlinear systems with input delays

In this paper, the problem of simultaneously reconstructing the states and delays for nonlinear systems subject to input delays is studied. To relax some limitations of the classical Lipschitz condition, the one-sided Lipschitz and quadratically inner-bounded conditions are employed to handle nonlinearities. The control inputs are subject to bounded unknown time-varying delays. To deal with this open and interesting problem, we propose a sliding mode observer based method to simultaneously estimate the states and identify the unknown delays of the systems without making assumption on differentiability of the delays. Furthermore, our method does not require the minimum phase condition that is common in sliding mode observer based schemes. The effectiveness of the proposed method is illustrated by a numerical example.