$H_{\infty }$ Asynchronous Admissibilization for Nonlinear Singular Delayed Hybrid Hydraulic Turbine Governing Systems With Impulsive Perturbations

Abstract

This article researches <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> asynchronous admissibilization for nonlinear singular delayed hybrid hydraulic turbine governing systems with impulsive perturbations. By exploiting Takagi-Sugeno (T-S) fuzzy technique, the fuzzy singular delayed hybrid hydraulic turbine governing system with impulsive perturbations is built, which can not only accurately and concisely describe the dynamic behaviors of the pipeline, but also resist damages for the hydraulic turbine system caused by sudden reasons. Then, the asynchronous fuzzy state feedback controller (FSFC) is designed by using parallel distributed compensation (PDC) technique, and the asynchronous mechanism (AM) between the modes of FSFC and the modes of controlled plant is depicted by a hidden Markovian model. By constructing an improved timer-dependent (T-D) Lyapunov-Krasovskii (L-K) functional, the new criteria about <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> admissibilization for fuzzy singular delayed hybrid hydraulic turbine governing systems with impulsive perturbations can be acquired. The gains of asynchronous FSFC are expressed by solving linear matrix inequalities (LMIs). Impulsive operators are successfully generalized and extended from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbb {R}$</tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbb {R}^{n\times n}$</tex-math></inline-formula> , which makes the approach presented in this article more universal. Finally, the simulation results prove the correctness and availability of the method provided in this article.