Based on a result of stability for linear time varying systems, a sufficient condition for global stability that does not use Lyapunov theory has been established for a class of discrete Takagi–Sugeno fuzzy systems. The condition involves testing the norms of products of the matrices of the consequences. The approach seeks to determine if at an instant of time the system becomes a contraction mapping. Because the computation burden associated with these tests may become prohibitive, a necessary and sufficient condition for local stability is derived. In a way, this decreases the computational burden and allows to customize the test. A two-step iterative stabilization algorithm is then introduced. The problem involves norm minimization and a posteriori stability test. Numerical examples are presented to demonstrate the applicability of the approach.

中文翻译：

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一类离散Takagi Sugeno模糊系统的矩阵范数、稳定性和稳定性

基于线性时变系统稳定性的结果，对一类离散Takagi-Sugeno模糊系统建立了不使用Lyapunov理论的全局稳定性的充分条件。该条件涉及测试结果矩阵的乘积规范。该方法试图确定系统是否在某个时刻成为收缩映射。由于与这些测试相关的计算负担可能变得过高，因此推导出局部稳定性的必要和充分条件。在某种程度上，这减少了计算负担并允许自定义测试。然后引入两步迭代稳定算法。该问题涉及范数最小化和后验稳定性测试。给出了数值例子来证明该方法的适用性。