SOS Based Robust <inline-formula> <tex-math notation="TeX">${\cal H}_{\infty}$ </tex-math></inline-formula> Fuzzy Dynamic Output Feedback Control of Nonlinear Networked Control Systems
针对离散时间非线性网络控制系统，提出一种模糊动态输出反馈控制器设计方法，允许控制器与系统的隶属函数和前提变量不同，且马尔可夫转移概率部分已知，通过平方和不等式求解控制器存在条件。
In this paper, a methodology for designing a fuzzy dynamic output feedback controller for discrete-time nonlinear networked control systems is presented where the nonlinear plant is modelled by a Takagi-Sugeno fuzzy model and the network-induced delays by a finite state Markov process. The transition probability matrix for the Markov process is allowed to be partially known, providing a more practical consideration of the real world. Furthermore, the fuzzy controller's membership functions and premise variables are not assumed to be the same as the plant's membership functions and premise variables, that is, the proposed approach can handle the case, when the premise of the plant are not measurable or delayed. The membership functions of the plant and the controller are approximated as polynomial functions, then incorporated into the controller design. Sufficient conditions for the existence of the controller are derived in terms of sum of square inequalities, which are then solved by YALMIP. Finally, a numerical example is used to demonstrate the validity of the proposed methodology.