广义不确定时滞系统的鲁棒性能分析

Robust Performance Analysis of Uncertain Singular Time-Delay Systems

分析了一类广义不确定时滞系统一些具体的鲁棒性能。针对既存在状态滞后,又存在时变参数不确定性的系统,通过构造Lyapunov泛函,根据Lyapunov稳定性理论并结合线性矩阵不等式方法,给出了既能使系统鲁棒稳定又能满足二次型性能指标的条件,并且将该条件转化成等价的线性矩阵不等式可行性问题,还给出了系统最小性能上界的求解方法,最后通过数值例子验证了该条件的可行性。

A detailed analysis of specific robustness properties pertaining to a category of uncertain singular time-delay systems is conducted,particularly focusing on systems characterized by both time delay and time-varying parameter uncertainty.By leveraging the construction of a Lyapunov functional and drawing upon Lyapunov stability theory in conjunction with the linear matrix inequality method,a methodology is presented to confer robust stability upon the system,while concurrently ensuring satisfaction of a quadratic performance index.The established condition is reformulated into an equivalent linear matrix inequality feasibility problem,enabling the determination of the upper bound of the minimum system performance through a structured solving approach.