论文标题
通过线路积分和新的Hessian矩阵估算的ITôStochasticT-S模型的稳定
Stabilization of Itô Stochastic T-S Models via Line Integral and Novel Estimate for Hessian Matrices
论文作者
论文摘要
本文提出了一种积分lyapunov函数方法，用于稳定性分析和稳定ITô随机T-S模型。与确定性情况不同，该模型的稳定性分析需要与基本函数的部分衍生物有关的线积分lyapunov函数的Hessian矩阵的信息。通过引入一种新方法来处理这些部分衍生物，并使用与一号等级的状态依赖性矩阵的属性，可以通过线积分Lyapunov函数建立基础系统的稳定性条件。所获得的这些条件比基于二次lyapunov函数的条件更一般。基于稳定性条件，通过锥形互补性布线化算法开发控制器。因此，提出了一种非二次lyapunov功能方法，用于ITôStochasticT-S模型的稳定问题。已经表明，可以通过优化具有线性约束的矩阵变量产物的痕迹总和来解决该问题。给出了数值示例以说明拟议的控制方案的有效性。
This paper proposes a line integral Lyapunov function approach to stability analysis and stabilization for Itô stochastic T-S models. Unlike the deterministic case, stability analysis of this model needs the information of Hessian matrix of the line integral Lyapunov function which is related to partial derivatives of the basis functions. By introducing a new method to handle these partial derivatives and using the property of state-dependent matrix with rank one, the stability conditions of the underlying system can be established via a line integral Lyapunov function. These conditions obtained are more general than the ones which are based on quadratic Lyapunov functions. Based on the stability conditions, a controller is developed by cone complementarity linerization algorithm. A non-quadratic Lyapunov function approach is thus proposed for the stabilization problem of the Itô stochastic T-S models. It has been shown that the problem can be solved by optimizing sum of traces for a group of products of matrix variables with linear constraints. Numerical examples are given to illustrate the effectiveness of the proposed control scheme.
