We explicitly construct global strict Lyapunov functions for rapidly time-varying nonlinear control systems. The Lyapunov functions we construct are expressed in terms of oftentimes more readily available Lyapunov functions for the limiting dynamics which we assume are uniformly globally asymptotically stable. This leads to new sufficient conditions for uniform global exponential, uniform globa...

We explicitly construct global strict Lyapunov functions for rapidly time-varying nonlinear control systems. The Lyapunov functions we construct are expressed in terms of oftentimes more readily available Lyapunov functions for the limiting dynamics which we assume are uniformly globally asymptotically stable. This leads to new sufficient conditions for uniform global exponential, uniform globa...

We explicitly construct global strict Lyapunov functions for rapidly time-varying nonlinear control systems. The Lyapunov functions we construct are expressed in terms of oftentimes more readily available Lyapunov functions for the limiting dynamics which we assume are uniformly globally asymptotically stable. This leads to new sufficient conditions for uniform global exponential, uniform globa...

We explicitly construct global strict Lyapunov functions for rapidly time-varying nonlinear control systems. The Lyapunov functions we construct are expressed in terms of oftentimes more readily available Lyapunov functions for the limiting dynamics which we assume are uniformly globally asymptotically stable. This leads to new sufficient conditions for uniform global exponential, uniform globa...

Stability has been explored to study the performance of learning algorithms in recent years and it has been shown that stability is sufficient for generalization and is sufficient and necessary for consistency of ERM in the general learning setting. Previous studies showed that AdaBoost has almost-everywhere uniform stability if the base learner has L1 stability. The L1 stability, however, is t...

In this paper, linear stability analysis of non-prismatic beam resting on uniform Winkler-Pasternak elastic foundation is carried out based on Eringen's non-local elasticity theory. In the context of small displacement, the governing differential equation and the related boundary conditions are obtained via the energy principle. It is also assumed that the width of rectangle cross-section varie...

We introduce a new notion of algorithmic stability, which we call training stability. We show that training stability is sufficient for good bounds on generalization error. These bounds hold even when the learner has infinite VC dimension. In the PAC setting, training stability gives necessary and sufficient conditions for exponential convergence, and thus serves as a distribution-dependent ana...

The work handles a Fredholm integro-differential equation involving boundary layers. A fitted second-order difference scheme has been created on uniform mesh utilizing interpolating quadrature rules and exponential basis functions. stability convergence of the proposed discretization technique are analyzed one example is solved to display advantages presented technique.

In this paper we will consider the control of spacecraft in a leader-follower formation using attitude measurements only. To analyze the formation under nonvanishing disturbances, we make use of the concept of uniform semiglobal practical exponential stability. To ease the Lyapunov analysis a new theorem is provided, giving sufficient conditions for systems presenting a cascaded structure to sa...