This paper presents the problem of robust and nonfragile stabilization of nonlinear systems described by multivariable Hammerstein models. The objective is focused on the design of a nonfragile feedback controller such that the resulting closed-loop system is globally asymptotically stable with robust disturbance attenuation in spite of controller gain variations. First, the parameters of linear and nonlinear blocks characterizing the multivariable Hammerstein model structure are separately estimated by using a subspace identification algorithm. Second, approximate inverse nonlinear functions of polynomial form are proposed to deal with nonbijective invertible nonlinearities. Thereafter, the Takagi–Sugeno model representation is used to decompose the composition of the static nonlinearities and their approximate inverses in series with the linear subspace dynamic submodel into linear fuzzy parts. Besides, sufficient stability conditions for the robust and nonfragile controller synthesis based on quadratic Lyapunov function, criterion, and linear matrix inequality approach are provided. Finally, a numerical example based on twin rotor multi-input multi-output system is considered to demonstrate the effectiveness.

中文翻译：

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多变量Hammerstein模型描述的非脆弱稳定非线性系统

本文提出了由多变量Hammerstein模型描述的非线性系统的鲁棒性和非脆弱性稳定问题。目标集中在非脆弱反馈控制器的设计上，以使所产生的闭环系统具有鲁棒性，全局渐近稳定尽管控制器增益变化，但干扰衰减仍然存在。首先，使用子空间识别算法分别估计表征多变量Hammerstein模型结构的线性和非线性块的参数。其次，提出了多项式形式的近似逆非线性函数来处理非双射可逆非线性。此后，使用Takagi–Sugeno模型表示将与线性子空间动态子模型串联的静态非线性及其近似逆的组成分解为线性模糊部分。此外，对于基于二次Lyapunov函数的鲁棒且非脆弱的控制器综合，具有足够的稳定性条件，准则，并提供线性矩阵不等式方法。最后，以一个基于双转子多输入多输出系统的数值例子为例，证明了该方法的有效性。