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In this paper the H∞ observers design problem for a class of discrete time Lipschitz nonlinear singular systems is considered. The approach is based on the parameterization of the obtained algebraic constraints from the estimation errors. Sufficient conditions for the existence of the observers which guarantee stability and the worst case observers error energy over all bounded energy disturbances is minimized are given. The method also unifies the design for the fullorder, reduced-order, minimal-order observers for discrete time systems. Application to standard systems with unknown input is presented via a numerical example.

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We present a new secured data transmission based on a chaotic synchronization and observability singularity. For this, we adopt an approach based on an inclusion of the message in the system structure and we use a sliding mode observer for system with unknown input in order to recover the information. We end the paper with an example of chaotic system with an observability bifurcation. Moreover, this example highlights some benefits of the so-called step-by-step sliding mode observer.