Sistemas de controle em domínios estratificados - Aquino, Paola Geovanna Patzi [UNESP] (2015)
In this work will characterize dynamical systems in the form of the so-called strati ed domain. Bressan and Hong [9] were the rst to de ne and work in strati ed domains. Roughly speaking, these are a collection of disjoint domains, each having its own dynamics; but not requiring that their domains are proximally smooth and not wedged. These terms were introduced by P. Wolenski and R. Barnard in [10]. At rst, we will establish Hamiltonian conditions to characterize weak and strong invariance for systems non-Lipschitz in strati ed domains. Secondly, we study the Hamiltonian conditions for systems weakly and strongly de- creasing and present conditions that guarantee global asymptotic stability for a strati ed dynamics and nally we present the problem Mayer type in strati ed domains where we show that the value function is the unique lower semicontinuous solution of an appropriate generalization of the classical Hamilton-Jacobi-Bellman equation for strati ed dynamics