H_∞ Finite-time Boundedness for Discrete-time Delay Neural Networks via Reciprocally Convex Approach

This paper addresses the problem of finite-time boundedness for discrete-time neural networks with interval-like time-varying delays. First, a delay-dependent finite-time boundedness criterion under the finite-time performance index for the system is given based on constructing a set of adjusted Lyapunov–Krasovskii functionals and using reciprocally convex approach. Next, a sufficient condition is drawn directly which ensures the finite-time stability of the corresponding nominal system. Finally, numerical examples are provided to illustrate the validity and applicability of the presented conditions. Keywords: Discrete-time neural networks, performance, finite-time stability, time-varying delay, linear matrix inequality.

Stability of Uncertain 2-D Discrete Systems in Presence of Generalized Overflow Nonlinearities

Stability analysis of two-dimensional (2-D) discontinuous systems with generalized overflow nonlinear effects is considered in this work. The 2-D models considered are the well-known Fornasini Marchesini Second Local State-Space (FMSLSS) model and the Roesser model. The effect of uncertainties and interim-like variable time-delays on the system is also examined in the study. Using reciprocally convex approach we provide stability criteria which is organized as matrix inequalities. Numerical illustrations are given to demonstrate the applicability of the results.

Exponential Stabilization of a Class of Time-Varying Delay Systems with Nonlinear Perturbations

This paper addresses the problem of exponential stabilization of a class of time-varying delay systems with nonlinear perturbations. These perturbations are related not only with current statextand the delayed statext−htbut also withβt, whereβtis a continuous function defined on[0,+∞). With the delay interval divided into two equidistant subintervals, a novel Lyapunov functional is introduced, and several new exponential stabilization criteria are derived in terms of linear matrix inequalities (LMIs) by employing reciprocally convex approach. Two examples are given to illustrate the effectiveness of the main results.