Hybrid Feedback Control for Exponential Stability and Robust <i>H</i>_∞ Control of a Class of Uncertain Neural Network with Mixed Interval and Distributed Time-Varying Delays

• Main Authors: Charuwat Chantawat, Thongchai Botmart, Rattaporn Supama, Wajaree Weera, Sakda Noinang
• Format: Article
• Language: English
• Published: MDPI AG 2021-05-01
• Series: Computation
• Subjects: neural networks; <i>H_∞</i> control; hybrid feedback control; mixed time-varying delay
• Online Access: https://www.mdpi.com/2079-3197/9/6/62

This paper is concerned the problem of robust <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mo>∞</mo></msub></semantics></math></inline-formula> control for uncertain neural networks with mixed time-varying delays comprising different interval and distributed time-varying delays via hybrid feedback control. The interval and distributed time-varying delays are not necessary to be differentiable. The main purpose of this research is to estimate robust exponential stability of uncertain neural network with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mo>∞</mo></msub></semantics></math></inline-formula> performance attenuation level <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>. The key features of the approach include the introduction of a new Lyapunov–Krasovskii functional (LKF) with triple integral terms, the employment of a tighter bounding technique, some slack matrices and newly introduced convex combination condition in the calculation, improved delay-dependent sufficient conditions for the robust <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mo>∞</mo></msub></semantics></math></inline-formula> control with exponential stability of the system are obtained in terms of linear matrix inequalities (LMIs). The results of this paper complement the previously known ones. Finally, a numerical example is presented to show the effectiveness of the proposed methods.