IEEE Trans Cybern. 2018 Sep;48(9):2723-2735. doi: 10.1109/TCYB.2017.2749239. Epub 2017 Dec 4.
This paper addresses the problem of delay-dependent robust and reliable $\mathscr {H}{\infty }$ static output feedback (SOF) control for a class of uncertain discrete-time Takagi-Sugeno fuzzy-affine (FA) systems with time-varying delay and actuator faults in a singular system framework. The Markov chain is employed to describe the actuator faults behaviors. In particular, by utilizing a system augmentation approach, the conventional closed-loop system is converted into a singular FA system. By constructing a piecewise-Markovian Lyapunov-Krasovskii functional, a new $\mathscr {H}{\infty }$ performance analysis criterion is then presented, where a novel summation inequality and S-procedure are succeedingly employed. Subsequently, thanks to the special structure of the singular system formulation, the piecewise-affine SOF controller design is proposed via a convex program. Lastly, illustrative examples are given to show the efficacy and less conservatism of the presented approach.
本文针对一类具有时变时滞和执行器故障的不确定离散时间 Takagi-Sugeno 模糊仿射（FA）系统，在奇异系统框架下，研究了时滞相关鲁棒可靠 $\mathscr{H}{\infty}$ 静态输出反馈（SOF）控制问题。利用马尔可夫链来描述执行器故障行为。具体来说，通过采用系统扩充方法，将传统的闭环系统转化为奇异 FA 系统。通过构造分段 Markov 李雅普诺夫-克拉索夫斯基泛函，提出了一种新的 $\mathscr{H}{\infty}$ 性能分析准则，其中成功应用了一种新的求和不等式和 S 过程。随后，由于奇异系统形式的特殊结构，通过凸规划提出了分段仿射 SOF 控制器设计。最后，通过实例说明了所提出方法的有效性和较小的保守性。
