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A sufficient condition for the stability of a system resulting from the interconnection of dynamical systems is given by the small gain theorem. Roughly speaking, to apply this theorem, it is required that the gains composition is continuous, increasing and upper bounded by the identity function. In this work, an alternative sufficient condition is… (More)

The problem under consideration is the synthesis of a distributed controller for a nonlinear network composed of input affine systems. The objective is to achieve exponential convergence of the solutions. To design such a feedback law, methods based on contraction theory are employed to render the controller-synthesis problem scalable and suitable to use… (More)

—This work provides an example that motivates and illustrates theoretical results related to a combination of small-gain and density propagation conditions. Namely, in case the small-gain fails to hold at certain points or intervals the density propagation condition can be applied to assure global stability properties. We repeat the theoretical results here… (More)

In this paper, the problem of stability analysis of a large-scale in-terconnection of nonlinear systems for which the small-gain condition does not hold globally is considered. A combination of the small-gain and density propagation inequalities is employed to prove almost input-to-state stability of the network.

- Humberto Stein Shiromoto, Vincent Andrieu, Christophe Prieur
- 2015

On considère une classe de systèmes non-linéaires pour lesquels la technique de synthèse par backstepping n'est pas applicable. On présente un critère pour la synthèse d'une commande hybride faisant l'union d'une commande par backstepping et d'une commande locale. Cette commande hybride rend le système bouclé globalement asymptotiquement stable. Le critère… (More)

In this paper we consider the problem of global asymptotic stabilization with prescribed local behavior. We show that this problem can be formulated in terms of control Lyapunov functions. Moreover, we show that if the local control law has been synthesized employing a LQ approach, then the associated Lyapunov function can be seen as the value function of… (More)

For an ISS system, by analyzing local and non-local properties, it is obtained different input-to-state gains. The interconnection of a system having two input-to-state gains with a system having a single ISS gain is analyzed. By employing the Small Gain Theorem for the local (resp. non-local) gains composition, it is concluded about the local (resp.… (More)

In the present work, we consider nonlinear control systems for which there exist structural obstacles to the design of classical continuous backstepping feedback laws. We conceive feedback laws such that the origin of the closed-loop system is not globally asymptotically stable but a suitable attractor (strictly containing the origin) is practically… (More)

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