连续时间T-S模糊系统的离散化:Delta算子方法

针对一类连续时间T-S模糊系统,利用Delta算子方法,对系统进行局部离散化和全局离散化处理.首先对模糊规则后件部分的线性时不变动态方程做局部离散化处理,然后再对系统的动态模型做全局离散化处理.为了获得T-S模糊系统的多胞结构,对全局离散化模型进行Taylor级数展开,从而得到近似全局离散化模型.基于线性矩阵不等式(LMI)技术,针对近似全局离散化模型设计了相应的状态反馈控制器,使系统被渐近镇定.采用Delta算子对连续系统离散化时,随着采样频率的加快,其离散模型将趋近于原来的连续模型,并保持原有的动力学性质.仿真结果验证了理论的有效性.

Discretization of Continuous-Time T-S Fuzzy System: Delta Operator Approach

The Delta operator approach is used to discretize a class of continuous-time T-S fuzzy systems.The linear time-invariable dynamic equation in the post-part of fuzzy rule is discretized locally,and then the fuzzy dynamic model of the system is discretized globally.To acquire the polyhedral structure of T-S fuzzy systems,the global discretization model is expanded using Taylor series to obtain an approximate global discretization model.Based on linear matrix inequality(LMI),a state-feedback controller is designed corresponding to approximate global discretization model so as to stabilize asymptotically the closed-loop system.Using the Delta operator to discretize the continuous systems,the discretization model tends to approach to the original continuous model with the increasing sampling frequency,while the original dynamical property is kept up.The simulation result verifies theoretically the validity of the approach proposed.