A cascade observer for a class of MIMO non uniformly observable systems with delayed sampled outputs

This paper investigates the observation problem for a class of MIMO non uniformly observable systems in the presence of sampled and delayed outputs. A high gain observer is first designed for the delay-free and continuous output measurement case. The observer gain involves the resolution of an appropriate Lyapunov differential equation allowing to show that the underlying observation error converges exponentially to zero under a well defined persistent excitation condition. This observer is then redesigned to cope with the output sampling process as well as the output delay thanks to an appropriate cascade structure composed of a set of dynamical subsystems. The first subsystem in the cascade is an impulsive continuous-discrete time observer which provides the estimation of the delayed state and each remaining subsystem in the cascade is a predictor which estimates the state over a small horizon equal to a fraction of the time delay in such a way that the state of the last predictor is an estimate of the system actual state. The exponential convergence to zero of the observation error related to the cascade observer is established for arbitrarily long delays provided that the maximum value of the sampling partition diameter is lower than a certain given bound. Simulations results are given to highlight the performance and the main properties of the proposed cascade observer. (C) 2016 Elsevier B.V. All rights reserved.