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摘要: 通过扩展常规Takagi-Sugeno模糊系统,定义了一类模糊奇异摄动系统,利用矩阵不等 式表达出了在摄动参数足够小时的闭环稳定性.镇定并行分布式补偿控制器增益和共同的Lyapunov 函数可利用两步法得到,并可分别归结于一组线性矩阵不等式和双线性矩阵不等式,后者 可以利用迭代线性矩阵不等式方法有效地求解.文末给出了数值和仿真实例.Abstract: This paper defines a fuzzy singularly perturbed system by extending the ordinary Takagi-Sugeno fuzzy model. Stability conditions for the fuzzy singularly perturbed systems for all small enough values of a singular perturbation parameter are derived and represented in terms of a set of matrix inequalities. By the proposed two-stage procedure, the stable parallel distributed compensation (PDC) feedback gains and a common Lyapunov function can be found. The outcome of the stabilization problem is recast into linear matrix inequalities(LMIs) and bilinear matrix inequalities (BMIs) in each stage respectively. The resulting BMIs can be effectively solved by the proposed iterative linear matrix inequality approach. Furthermore, numerical examples and simulation results are given to verify the effectiveness of the algorithms proposed above.
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