State Estimator and Observer Design of One-Sided Lipschitz Systems with Delayed Output

In this paper we study state observer problem for one-sided Lipschitz system with time-varying delay in output. We propose a new constructing approach of observer (or state estimator) that is composed of three components: delayed state observer, state predictor and state estimator. We prove rigorously convergence of the observer. The result shows that if
$(A, C)$
is exponentially detectable with rate
$\beta$
, then for anyone-sided Lipschitz system with constant
$\rho$
, we can construct an exponential-type state observer (or state estimator) provided
$\beta > \rho$
. As an illustration, we give two examples to show the effective of observer. The proposed method also is applied to study the existence of observer for other nonlinear systems with delayed output.