Finite time observation of nonlinear time-delay systems with unknown inputs

Causal and non-causal observability are discussed in this paper for nonlinear time-delay systems. By extending the Lie derivative for time-delay systems in the algebraic framework introduced by Xia et al. [2002], a canonical form and give sufficient condition in order to deal with causal and non-causal observations of state and unknown inputs of time-delay systems is presented.