广义非线性脉冲切换系统的指数稳定和L_(2)增益控制  

Exponential Stability and L_(2)-Gain Control of Nonlinear Pulse Switching Singular Systems

作　　者：杨冬梅[1] 李祉含 YANG Dong-mei;LI Zhi-han(School of Sciences,Northeastern University,Shenyang 110819,China)

机构地区：[1]东北大学理学院,辽宁沈阳110819

出　　处：《东北大学学报（自然科学版）》2021年第6期908-912,共5页Journal of Northeastern University(Natural Science)

基　　金：国家自然科学基金资助项目(61673100).

摘　　要：研究了一类具有脉冲的广义非线性切换系统的指数稳定问题和L_(2)增益控制问题.将脉冲以及非线性控制加入到系统当中,系统更具有实际意义.首先,提出了一种具有L_(2)增益控制的状态反馈控制器的有效设计方法,通过构建Lyapunov函数,改进系统中的状态反馈控制器,使得闭环系统是指数稳定的.其次,利用线性矩阵不等式并结合模型依赖平均驻留时间方法,给出了系统指数稳定且具有L_(2)增益性能的充分条件.最后,通过数值例子及图像仿真来说明理论结果的有效性.Exponential stability and L_(2)-gain control of singular nonlinear switching systems with pulses are studied.The pulse and nonlinear control are added to the system to make it of more practical significance.First,an effective design method of state feedback controller with L_(2)-gain control is proposed by constructing the Lyapunov function,and the state feedback controller in the system is improved to make the closed-loop system exponentially stable.Secondly,by using the linear matrix inequality and the model dependent average dwell time method,the sufficient conditions for exponential stability and L_(2)-gain performance are given.Finally,numerical examples and image simulation are given to illustrate the effectiveness of the theoretical results.

关 键 词：广义系统 指数稳定性 LYAPUNOV函数 L_(2)增益 脉冲 平均驻留时间 

分 类 号：O231[理学—运筹学与控制论]