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We address stabilization problems of networked control systems in the presence of bounded packet losses and time-varying network-induced delays. When the delay is less than the transmission interval, we prove that the stability of the closed-loop system is implied by that of a switched system. Based on theories on switched systems, we present stabilizing conditions by using packet-loss-dependent Lyapunov functions, and design multiple controllers depending on the packet loss and the network-induced delay. Furthermore, based on the stabilizing conditions, we discuss the robustness of the stabilization against the packet loss and the network-induced delay. Several numerical examples and simulations are worked out to demonstrate the effectiveness of the proposed design approach.

In this article, we investigate some Cauchy problems associated with Helmholtz-type equations in rectangle using the method of truncation. Not alike the previous literature, we propose to choose the regularization parameter by an a posteriori rule, with which we can obtain error estimates of Holder-type between the exact solution and their regularized approximation. Numerical simulations show that the proposed scheme is effective and stable.

This paper is devoted to a new regularization method for solving the numerical analytic continuation of an analytic function $f(z)=f(x+iy)$ on a strip domain $\Omega^+=\{z=x+iy\in \mathbb{C}\mid x\in \mathbb{R}, 0

We propose a numerical reconstruction method for solving a time-fractional backward heat conduction problem. Based on the idea of reproducing kernel approximation, we reconstruct the unknown initial heat distribution from a finite set of scattered measurements of transient temperature at a fixed final time. The standard Tikhonov regularization technique using the norm of reproducing the kernel Hilbert space as the penalty term is adopted to provide a stable solution when the measurement data contains noise. Numerical results indicate that the proposed method is efficient.

The ill-posed problem of attempting to recover the temperature functions from one measured transient data temperature at some interior point of a one-dimensional semi-infinite conductor when the governing linear diffusion equation is of fractional type is discussed. A simple regularization method based on Dirichlet kernel mollification techniques is introduced. We also proposea priorianda posterioriparameter choice rules and get the corresponding error estimate between the exact solution and its regularized approximation. Moreover, a numerical example is provided to verify our theoretical results.