Relaxed stabilisation criterion for discrete T–S fuzzy systems by minimum-type piecewise non-quadratic Lyapunov function
Relaxed stabilisation criterion for discrete T–S fuzzy systems by minimum-type piecewise non-quadratic Lyapunov function
复制标题
最小型分段非二次 Lyapunov 函数离散 T-S 模糊系统的松弛稳定准则
DOI：
10.1049/iet-cta.2010.0697
复制
发表时间：
2012
影响因子：
2.6
通讯作者：
Hua O. Wang
中科院分区：
文献类型：
--
作者：
Y. Chen;H. Ohtake;Kazuo Tanaka;Wen;Hua O. Wang
为了得到松弛的结果，文献中采用分段李雅普诺夫函数和非二次李雅普诺夫函数分析了T-S模糊系统。然而，到目前为止，分段非二次李雅普诺夫函数还没有被用来设计T-S模糊控制系统。基于上述考虑，本研究利用最小型分段非二次李雅普诺夫函数设计离散T-S模糊控制系统。基于分段非二次李雅普诺夫函数，提出了切换非并行分布补偿控制律，以获得松弛镇定准则。由于该准则的某些条件是双线性矩阵不等式条件，采用粒子群优化算法求解该准则。最后通过算例验证了该准则的有效性。
Piecewise Lyapunov functions and non-quadratic Lyapunov functions have been employed to analyse Takagi–Sugeno (T–S) fuzzy systems for getting relaxed results in the literature. Nevertheless, until now piecewise non-quadratic Lyapunov functions have not been used to design T–S fuzzy control systems. Motivated by the aforementioned concerns, this study utilises the minimum-type piecewise non-quadratic Lyapunov function to design the discrete T–S fuzzy control system. Based on the piecewise non-quadratic Lyapunov function, the switching non-parallel distributed compensation control law is proposed to obtain the relaxed stabilisation criterion. Owing to that some conditions of the proposed criterion are bilinear matrix inequalitiy conditions, the particle swarm optimisation algorithm is applied for finding out the solution of the criterion. An example is provided to illustrate the effectiveness of the proposed criterion.