The main goal of this article is to use properties of homogeneous systems for addressing the problem of stability for a class of nonlinear systems with sampled-data inputs. This nonlinear strategy leads to several kinds of stability, i.e. local asymptotic stability, global asymptotic stability or global asymptotic set stability, depending on the sign of the degree of homogeneity. The results are illustrated with the case of the double integrator.

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This paper is concerned with the leader-following consensus problem for a class of Lipschitz nonlinear multi-agent systems with uncertain dynamics, where each agent only transmits its noisy output, at discrete instants and independently from its neighbors. The proposed consensus protocol is based on a continuous-discrete time observer, which provides a continuous time estimation of the state of the neighbors from their discrete-time output measurements, together with a continuous control law. The stability of the multi-agent system is analyzed with a Lyapunov approach and the exponential practical convergence is ensured provided that the tuning parameters and the maximum allowable sampling period satisfy some inequalities. The proposed protocol is simulated on a multi-agent system whose dynamics are ruled by a Chua's oscillator.

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