This paper details the stability analysis of the continuous-time Kalman filter dynamics for linear timevarying systems subject to exponentially decaying perturbations. It is assumed that estimates of the input, output, and matrices of the system are available, but subject to unknown perturbations which decay exponentially with time. It is shown that if the nominal system is uniformly completely...

We obtain sharp pointwise error estimates for relaxation approximation to scalar conservation laws with piecewise smooth solutions. We first prove that the first-order partial derivatives for the perturbation solutions are uniformly upper bounded (the so-called Lip+ stability). A one-sided interpolation inequality between classical L1 error estimates and Lip+ stability bounds enables us to conv...

We study the surface diffusion flow acting on a class of general (non–axisymmetric) perturbations of cylinders Cr in IR3. Using tools from parabolic theory on uniformly regular manifolds, and maximal regularity, we establish existence and uniqueness of solutions to surface diffusion flow starting from (spatially–unbounded) surfaces defined over Cr via scalar height functions which are uniformly...

We give a proof of the Poincaré inequality in W (Ω) with a constant that is independent of Ω ∈ U , where U is a set of uniformly bounded and uniformly Lipschitz domains in R. As a byproduct, we obtain the following : The first non vanishing eigenvalues λ2(Ω) of the standard Neumann (variational) boundary value problem on Ω for the Laplace operator are bounded below by a positive constant if the...

In this paper, we investigate the boundedness and uniformly asymptotically stability of solutions to a certain third order non-autonomous differential equations with bounded delay. By constructing Lyapunov functional, sufficient conditions for considered are obtained. We used an example demonstrate feasibility our results. The results essentially improve, include, complement in literature.

For a class of single-input single-output continuous-time nonlinear systems, a three-layer neural network-based controller that feedback linearizes the system is presented. Control action is used to achieve tracking performance for a feedback linearizable but unknown nonlinear system. The control structure consists of a feedback linearization portion provided by two neural networks plus a robus...

Uniform measures are defined as the functionals on the space of bounded uniformly continuous functions that are continuous on bounded uniformly equicontinuous sets. If every cardinal has measure zero then every countably additive measure is a uniform measure. The functionals sequentially continuous on bounded uniformly equicontinuous sets are exactly uniform measures on the separable modificati...

In a number of papers ([1], [2]), Delves and Mead have derived some useful (though limited) rate of convergence results which can be applied to variational approximations for the solution of linear positive definite operator equations when the coordinate system is uniformly asymptotically diagonal. Independently, Mikhlin [5] has examined the stability of such variational approximations in the c...