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In this paper, we consider the issue of stabilizing a class of linear systems using irregular sampled output measurements. For this purpose, we design a standard linear state feedback controller and an impulsive observer to provide an estimate the non-measured states, which are subsequently fed back in the control algorithm. We consider linear systems that can be decomposed, via a change of coordinates, into their respective measured and unmeasured dynamics. We consider the two cases whereby the unmeasured subspace is stable and unstable respectively. In the case where the unmeasured subspace is stable, we employ a standard impulsive observer coupled with a continuous linear feedback control. Next, when the unmeasured subspace is unstable, we employ two cascaded observers-an impulsive and a Luenberger observer-in conjunction with a linear feedback control. In order to prove the stability of the overall closed-loop system we proposed a practical stability result for a class of linear impulsive systems. Some simulation results are presented to show the performance of the observer-based control. Finally, some conclusions are drawn.

In this paper, a new method of strange attractor identification, under sparse measurement, is proposed this method is based on the concept of compressive sensing. For this, some particular impulsive observers have been presented and adding a decision scheme linked to diagnosis method, the identification of the strange attractor and state observation are done. Some simulations results are given in order to highlight the well founded of the proposed design.

This paper proposes a new observer scheme for chaotic and hyperchaotic systems. Firstly, a classical impulsive observer is investigated for Lorenz chaotic system. This approach is based on sufficient conditions for stability of impulsive dynamical systems. After, an hybrid observer is proposed for hypoerchaotic systems. Simulation results highlight the well founded of such observer design and show that the discrete measurement may be eventually sparse.