The implicit midpoint rules are employed as a powerful numerical technique, and in this article we attend class of viscosity iteration approximations on hierarchical problems for the double rules. We prove strong convergence theorem to unique solution problem technique is established under some favorable conditions imposed control parameters Hilbert spaces. Furthermore, propose applications con...

Part I of this paper introduced the notion of implicit Lagrangian systems and their geometric structure was explored in the context of Dirac structures. In this part, we develop the variational structure of implicit Lagrangian systems. Specifically, we show that the implicit Euler-Lagrange equations can be formulated using an extended variational principle of Hamilton called the Hamilton-Pontry...

In this paper, an extension of algorithm for the implicit discretization a super-twisting sliding mode observer is presented. Implicit and explicit algorithms homogeneous differentiators, where no physical model information considered, are investigated in literature. This article studies behavior when considering models rather general class nonlinear systems. The discrete equations reformulated...