New Admissibility and Admissibilization Criteria for Nonlinear Discrete-Time Singular Systems by Switched Fuzzy Models
针对非线性离散时间奇异系统，通过划分隶属函数和尺度变换建立等效切换模糊系统，利用分段Lyapunov函数和奇异值分解推导出松弛的稳定性准则，并设计两类切换控制器确保闭环系统容许性。
Admissibility analysis and control synthesis for nonlinear discrete-time singular systems are considered in this article. With regard to the type-1 and interval type-2 fuzzy singular systems, the partition of membership functions and scale transform is imposed, and new switched fuzzy systems, which are equivalent to the original systems, are established. A relaxed stability criterion is derived to ensure the admissibility of the system by using the piecewise Lyapunov function and singular value decomposition. Moreover, two classes of switched controllers are designed for the systems. One is for type 1 systems and the membership functions are consistent with those of the systems. The other can be applied to both of the fuzzy systems by introducing linear membership functions in each subregion. Two criteria are obtained to guarantee that the closed-loop systems are admissible. Several illustrative examples are provided to show the effectiveness of the developed methods.