离散模糊系统的二次稳定控制器设计

Quadratic stable controller design of discrete fuzzy systems

为了研究离散T-S模糊系统的二次稳定控制问题,在输入采用双交叠模糊分划的模糊系统的相关性质的基础上,从最大交叠规则组中构造一个离散型的分段Lyapunov函数,并证明了一个新的判定闭环离散模糊控制系统稳定性的充分条件,该条件仅需在每个最大交叠规则组中分别寻找各自公共的正定矩阵。较之以往稳定性判定方法,此方法不仅克服了需要寻找一个公共矩阵的不足,而且也减少了求解Lyapunov不等式的个数。应用并行分布补偿原理设计出使模糊系统全局渐近稳定的控制器,并以一个船舶运动系统为例进行仿真,结果验证了该控制器的有效性。

For the quadratic stable problem of discrete T-S fuzzy systems, a discrete piecewise Lyapunov function was constructed in maximal overlapped-rule groups based on the properties of fuzzy systems with two-overlapped fuzzy partition inputs. And then a new sufficient condition to check the stability of discrete closed-loop T-S fuzzy systems was proposed and proved. This condition only requires finding a common positive definite matrix in each maximal overlapped-rule group. Compared with former stability analysis approaches, this approach can not only overcome the defect of finding a common positive definite matrix but also reduce the number of solving Lyapunov inequalities. In addition, a fuzzy controller was designed to acquire global asymptotically stable fuzzy system models by means of the parallel distributed compensation approach. Finally, for a ship motion system, simulation results demonstrate that the ratic stable controller is effective. proposed quadratic stable controller is effective.