正奇异半马尔可夫跳变时滞系统的状态反馈执行器饱和控制  

State-feedback control for singular positive semi-Markov jump time-delay systems with actuator saturation

作　　者：任雪静 李博 赵俊杰 Ren Xuejing;Li Bo;Zhao Junjie(School of Sciences,Changzhou Institute of Technology,Changzhou 213032,China;School of Electrical and Information Engineering,Jiangsu University of Technology,Changzhou 213001,China)

机构地区：[1]常州工学院理学院,江苏常州213032 [2]江苏理工学院电气信息工程学院,江苏常州213001

出　　处：《南京理工大学学报》2025年第2期174-182,共9页Journal of Nanjing University of Science and Technology

基　　金：国家自然科学基金(11901061;61903166;61803186)。

摘　　要：针对实际工程中普遍存在的执行器饱和、系统时变时滞因素,提出了一类正奇异半马尔可夫跳变系统(SPSMJS)的控制器设计方法。首先,设计状态反馈控制器与辅助函数处理执行器饱和对系统的影响,深入分析随机跳变行为如何影响模态依赖奇异系统的状态不连续性,利用矩阵分解法得出一个随机稳定性判别的重要引理。然后,基于饱和引理和Lyapunov稳定性理论构造Lyapunov-Krasovskii泛函,利用线性矩阵不等式方法证明了闭环系统均方意义下实现指数稳定的充分条件,并提出新的控制器设计算法。结合定理设计出寻优算法,能够估计出在饱和条件下系统保持稳定的最大吸引域,即可使算法适用范围扩大到系统初值邻域上界大于1的情况。最后,在仿真算例中闭环系统状态满足正系统条件且在0~2 s快速收敛稳定,控制器状态曲线满足0.5的预设饱和条件,表明控制算法在复杂因素系统中是有效的。仿真算例说明了控制算法的有效性。To address the common factors of actuator saturation and system time-varying delay in actual engineering,a controller design method for a class of singular positive semi-Markov jump systems(SPSMJS)is proposed.Firstly,a state-feedback controller and an auxiliary function are designed to deal with the impact of actuator saturation on the system.The influence of random jump behavior on the state discontinuity of the mode dependent singular system is deeply analyzed,and an important lemma for stochastic stability is given by matrix decomposition method.Then,based on the saturation lemma and Lyapunov stability theory,a Lyapunov-Krasovskii function is constructed.The sufficient conditions for the mean square exponential stability of closed-loop system are proved by using linear matrix inequality method,and a new controller design algorithm is proposed.Combined with the theorem,an optimization algorithm is designed,which can estimate the maximum attractive domain where the system remains stable under saturation conditions,thus the scope of application of the algorithm can be expanded to the case where the upper bound of the initial value neighborhood of the system is greater than 1.Finally,in a simulation example,the closed-loop system satisfies the conditions of a positive system and rapidly converges to stability within 0-2 s.The controller state curve meets the preset saturation condition of 0.5,indicating that the control algorithm is effective in complex factor systems.Simulation examples demonstrate the effectiveness of the control algorithm.

关 键 词：正系统 执行器饱和 时滞系统 奇异半马尔可夫跳变系统 

分 类 号：TP273.1[自动化与计算机技术—检测技术与自动化装置]