离散模糊时滞系统时滞相关稳定性判别与控制

Delay-dependent stability criteria and control of discrete fuzzy systems with time delay

针对具有时变时滞的离散Takagi-Sugeno(T-S)模糊系统,提出一种新的时滞相关稳定性判别和控制器设计方法,以降低以往方法的保守性和难度。首先,在各个最大交叠规则组中构造一种新的分段离散型Lyapunov-Krasovskii函数。然后,提出和证明分别判定具有时变时滞的开环离散T-S模糊系统和闭环离散T-S模糊系统时滞相关稳定性的新的充分条件。并且,在运用并行分布补偿控制策略的基础上,设计具有时变时滞的闭环离散T-S模糊系统的模糊控制器。由于上述两个时滞相关稳定性的充分条件仅需在每个最大交叠规则组中分别寻找各自的公共矩阵,因此不仅克服了在整个可行域中需要寻找公共矩阵的缺陷,而且也减少了求解线性矩阵不等式的个数。最后,仿真示例验证此方法的有效性和优越性。

For discrete Takagi-Sugeno （T-S） fuzzy systems with the time-varying delay, an approach of checking the delay-dependent stability and designing the delay-dependent controller is proposed to reduce the conservatism and the difficulty of the former approaches. Firstly, a piecewise discrete Lyapunov-Kra- sovskii function in each maximal overlapped-rule group was constructed. Then the delay-dependent suffi- cient criteria to check the stabilities of open-loop discrete T-S fuzzy systems and closed-loop discrete T-S fuzzy systems with the time-varying delay were proposed and proved. Furthermore, the design of fuzzy controllers of closed-loop discrete T-S fuzzy systems with the time-varying delay was investigated via paral- lel distributed compensation control scheme. As the above two delay-dependent sufficient criteria only re- quire finding common matrices in each maximal overlapped-rule group, these proposed sufficient criteria overcome the defect of finding common matrices in the whole feasible region but also reduce the number of solving linear matrix inequalities. At last, a simulation example shows that the proposed approach is ef- fective and advantageous.