非线性广义半马尔可夫跳跃系统的H∞控制
H∞ Control of Nonlinear Singular Semi-Markov Jump Systems
摘要: 探讨一类非线性广义半Markov跳跃系统的随机稳定性和H∞控制问题。设计新型的Lyapunov-Krasovkii泛函(LKF)，用于减少冗余决策变量。同时，引入参数依赖的互凸矩阵不等式(PDRCMI)来降低保守性，保证了非线性广义Markov跳跃系统渐进稳定并满足性能，最后，通过数值算例验证了所得方法的有效性。
Abstract: The stochastic stability of a class of nonlinear singular semi-Markov jumping systems and H∞ control problems are discussed. A new type of Lyapunov-Krasovkii functional (LKF) is designed to reduce redundant decision variables. At the same time, the parameter-dependent Convex Matrix Inequality (PDRCMI) is introduced to reduce the conservatism, which ensures the asymptotic stability and satisfies the performance of the nonlinear singular Markov jumping system, and finally, the effectiveness of the proposed method is verified by numerical examples.
文章引用：鲁禹, 郑成德. 非线性广义半马尔可夫跳跃系统的H∞控制[J]. 应用数学进展, 2024, 13(6): 2952-2965. https://doi.org/10.12677/aam.2024.136282

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