An SOS-based stable control of polynomial discrete fuzzy systems
An SOS-based stable control of polynomial discrete fuzzy systems
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DOI：
10.1109/acc.2008.4587266
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发表时间：
2008-06
期刊：
影响因子：
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通讯作者：
Kazuo Tanaka;H. Ohtake;Hua O. Wang
中科院分区：
文献类型：
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作者：
Kazuo Tanaka;H. Ohtake;Hua O. Wang
给出了多项式离散模糊系统的稳定性和镇定条件。首先，基于多项式Lyapunov函数，给出了无输入多项式离散模糊系统的稳定性条件。其次，给出了设计稳定多项式模糊控制器的镇定条件。它们都用SOS表示，并通过最近发展的SOSTOOLS进行数值(部分符号)求解。此外，多项式离散模糊系统和控制器还包含离散高木-宿野(T-S)模糊系统和控制器作为特例。因此，本文所讨论的方法比现有的基于线性矩阵不等式的离散T-S模糊控制系统设计方法更具一般性。为了说明该设计方法的有效性，给出了一个设计实例。这个例子说明了我们方法的实用性。
This paper presents stability and stabilization conditions of polynomial discrete fuzzy systems. First, based on polynomial Lyapunov functions, we derive a stability condition of polynomial discrete fuzzy systems without inputs. Secondly, we derive a stabilization condition to design a stable polynomial fuzzy controller. Both of them are represented in terms of SOS and are numerically (partially symbolically) solved via the recent developed SOSTOOLS. In addition, polynomial discrete fuzzy systems and controllers contain discrete Takagi-Sugeno (T-S) fuzzy systems and controllers as a special case. Hence, the approach discussed in this paper is more general than that based on the existing LMI approaches to discrete T-S fuzzy control system designs. To illustrate the validity of the design approach, a design example is provided. The example shows the utility of our approach.