Improved GeneralizedH2Filtering for Static Neural Networks with Time-Varying Delay via Free-Matrix-Based Integral Inequality

Abstract

This paper focuses on the generalized 2 filtering of static neural networks with a time-varying delay. The aim of this problem is to design a full-order filter such that the filtering error system is globally asymptotically stable with guaranteed 2 performance index. By constructing an augmented Lyapunov-Krasovskii functional and applying the free-matrix-based integral inequality to estimate its derivative, an improved delay-dependent condition for the generalized 2 filtering problem is established in terms of LMIs. Finally, a numerical example is presented to show the effectiveness of the proposed method.

New Stability Criteria for Event‐Triggered Nonlinear Networked Control System with Time Delay

“…Afterwards, Wirtinger-based inequality which is considered a tighter method than Jensen inequality for estimation of the integral term was developed and employed in various systems [42]. In recent years, many researchers have improved the Wirtinger-based inequality approach, such as free-matrix-based integral inequality [43], auxiliary function-based integral inequality [44]. In this note, we will make use of a new integral inequality called Bessel-Legendre inequality together with reciprocally convex combination lemma to research the stability of nonlinear networked control system with time delay under improved event-triggered scheme.…”

Event‐Triggered Stability Analysis of Semi‐Markovian Jump Networked Control System with Actuator Faults and Time‐Varying Delay via Bessel–Legendre Inequalities

“…Besides, Wirtinger-based inequality, as a more advanced technology than Jensen inequality, was introduced in various control systems [22]. Moreover, free-matrix-based integral inequality was applied in [23] for researching filtering problem for the neural network system. A kind of integral inequality method based on auxiliary function was introduced in [24].…”