CAJ | 학술논문

研究了一类参数不确定的具有多个时滞的Lur′e型控制系统与时滞相关绝对稳定性问题.通过将原系统变换为等价的奇异系统,利用Moon不等式放大向量积,构造出一个新的Lyapunov-Krasovskii泛函.并由此基于线性矩阵不等式,得到了系统与时滞相关绝对稳定的充分条件.这些充分条件无须预调任何参数矩阵,可以直接运用Matlab软件中LMI工具箱求解.数值例子表明,与现有结果相比,本文结果较大地改进了保证不确定时滞Lur′e型控制系统绝对稳定的时滞界.
연구료일류삼수불학정적구유다개시체적Lur′e형공제계통여시체상관절대은정성문제.통과장원계통변환위등개적기이계통,이용Moon불등식방대향량적,구조출일개신적Lyapunov-Krasovskii범함.병유차기우선성구진불등식,득도료계통여시체상관절대은정적충분조건.저사충분조건무수예조임하삼수구진,가이직접운용Matlab연건중LMI공구상구해.수치례자표명,여현유결과상비,본문결과교대지개진료보증불학정시체Lur′e형공제계통절대은정적시체계.
This paper is concerned with delay-dependent absolute stability for a class of uncertain Lur′e systems with multiple time-delays. By using a descriptor model transformation of the system and by applying a recent result on bounding of cross products of vectors, a new type of Lyapunov-Krasovskii functional is constructed. Based on the new functional, delay-dependent sufficient conditions for absolute stability are derived in terms of linear matrix inequalities. These conditions do not require any parameter tuning, and can be solved numerically using the software LMI Lab. A numerical example is presented which shows that the proposed method can substantially improve the delay bound for absolute stability of Lur′e system with time-delays, compared to the existing ones.