<i>H</i> <sub>∞</sub>Adaptive Sliding-Mode Control for Nonlinear Delayed Singular Systems Under Impulsive Attacks via Piecewise Auxiliary Functions Method
Guangming Zhuang, Yiqun Liu, Xiangpeng Xie, Jianwei Xia
Abstract
This work addresses the issue of <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> adaptive sliding-mode control (SMC) for nonlinear delayed singular systems (NDSSs) under impulsive attacks (IAs). The NDSSs subjected to IAs are modeled as fuzzy delayed singular impulsive systems (FDSISs), and a neoteric fuzzy integral sliding surface function is constructed based on the piecewise auxiliary functions method, which is continuous on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(0,+\infty)$ </tex-math></inline-formula> without any other additional conditions. Then, a suitable SMC law and an adaptive SMC law are designed, such that the state trajectories of FDSIS can be driven to the predetermined sliding surface in finite time. In addition, an improved impulse-time-dependent Lyapunov-Krasovskii functional containing characteristics of IAs and time delays is designed, and it is demonstrated to be continuous along the FDSIS trajectories. Improved conditions are put forward in the form of strict linear matrix inequalities via congruent transformation technology, which can guarantee that the singular sliding-mode dynamics under IAs fulfills <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> stochastic admissibilization. Finally, the practicability of the approach presented is attested and the effects of IAs on convergence time are testified by the networked truck-trailer system.