线性时滞系统的时滞相关稳定性

本文讨论了线性时滞系统x(t)=Ax( ) Bx(t-τ)渐近稳定的时滞界限，利用Lyapunov—Krasovskii泛函及H∞范数理论，获得了线性时滞系统时滞相关稳定的充分条件，同时得到了一个新的时滞界限的代数估计式。将本文结果应用于实际系统，计算简单，并且扩大了时滞的稳定区域，降低了对时滞的保守性。分析结果还表明，线性时滞系统的稳定性可以转化为一定常无时滞的线性系统的H∞控制问题。

On Delay-dependent Stability for Linear Systems with Delay

The delay bounds of the systems described by )()()(t-+=tttBxAxx&under the condition of asymptotic stability are discussed. A new delay dependent condition is derived using the Lyapunov-Krasovskii functional method and H-infinite norm theory. A new algebraic appraisal expression about the system delay bounds is also deducted. Some examples demonstrate that the conclusion of this paper is useful, the calculation becomes easier, conservative property is smaller than that of previous theories[4-8] and the delay bounds become larger. Another useful conclusion is that the stability problem of the linear system with delay can be translated as a problem of the H-infinite control of a delay-free linear system.