A Gain-Scheduling Approach to Nonfragile H Fuzzy Control Subject to Fading Channels

• Published in: IEEE transactions on fuzzy systems Vol. 26; no. 1; pp. 142 - 154
• Main Authors: Zhang, Sunjie, Wang, Zidong, Ding, Derui, Wei, Guoliang, Alsaadi, Fuad E., Hayat, Tasawar
• Format: Journal Article
• Language: English
• Published: IEEE 01.02.2018
• Subjects: <named-content xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" content-type="math" xlink:type="simple"> <inline-formula> <tex-math notation="LaTeX"> H_\infty</tex-math> </inline-formula> </named-content> control; Fading channels; Fuzzy control; gain-scheduling control; Mathematical model; nonfragile control; Nonlinear systems; Random variables; randomly occurring gain variations (ROGVs); Symmetric matrices; Takagi–Sugeno (T–S) fuzzy systems
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2016.2641023

This paper deals with the nonfragile <inline-formula><tex-math notation="LaTeX">H_\infty</tex-math> </inline-formula> control problem for a class of discrete-time Takagi-Sugeno fuzzy systems with both randomly occurring gain variations (ROGVs) and channel fadings. The system measurement is subject to fading channels described by Rice fading model where the channel coefficients are random variables taking values within given intervals. The gain matrices of the output feedback controllers are subject to random fluctuations referred to as the ROGVs. The purpose of the addressed problem is to design a parameter-dependent nonfragile output-feedback controller such that, in the presence of both ROGVs and channel fadings, the closed-loop system is exponentially mean-square stable while achieving the guaranteed <inline-formula><tex-math notation="LaTeX">H_\infty</tex-math></inline-formula> disturbance attenuation level. A gain-scheduling approach is developed to tackle the addressed problem where the designed controller gains are dependent on certain parameters of practical significance (e.g., packet dropout rate). Through stochastic analysis and Lyapunov functional approach, sufficient conditions are derived for the existence of the desired output feedback controller ensuring both the exponential mean-square stability and the prescribed <inline-formula><tex-math notation="LaTeX">H_\infty</tex-math></inline-formula> performance. The explicit expression of the feedback controller is also characterized by using a semidefinite programming method. Finally, an illustrative example is given to show the usefulness and effectiveness of the proposed design method.