Department of Marine Engineering, National Taiwan Ocean University, Taiwan, Republic of China.
ISA Trans. 2011 Jan;50(1):37-43. doi: 10.1016/j.isatra.2010.10.003. Epub 2010 Oct 30.
The purpose of this paper is to study the H(∞) constrained fuzzy controller design problem for discrete-time Takagi-Sugeno (T-S) fuzzy systems with multiplicative noises by using the state observer feedback technique. The proposed fuzzy controller design approach is developed based on the Parallel Distributed Compensation (PDC) technique. Through the Lyapunov stability criterion, the stability analysis is completed to develop stability conditions for the closed-loop systems. Besides, the H(∞) performance constraints is also considered in the stability condition derivations for the worst case effect of disturbance on system states. Solving these stability conditions via the two-step Linear Matrix Inequality (LMI) algorithm, the observer-based fuzzy controller is obtained to achieve the stability and H(∞) performance constraints, simultaneously. Finally, a numerical example is provided to verify the applicability and effectiveness of the proposed fuzzy control approach.
本文旨在研究具有乘性噪声的离散时间 Takagi-Sugeno(T-S)模糊系统的 H(∞)约束模糊控制器设计问题,采用状态观测器反馈技术。所提出的模糊控制器设计方法是基于并行分布补偿(PDC)技术开发的。通过李雅普诺夫稳定性准则,完成了稳定性分析,为闭环系统建立了稳定性条件。此外,在稳定性条件的推导中还考虑了 H(∞)性能约束,以考虑干扰对系统状态的最坏影响。通过两步线性矩阵不等式(LMI)算法求解这些稳定性条件,得到基于观测器的模糊控制器,以实现稳定性和 H(∞)性能约束的同时满足。最后,通过一个数值例子验证了所提出的模糊控制方法的适用性和有效性。