时变时滞Lurie控制系统的绝对稳定性

基于Lyapunov稳定性定理,利用线性矩阵不等式方法给出了系统绝对稳定的判别准则.讨论了具有多个时变时滞的Lurie直接控制系统和Lurie间接控制系统的绝对稳定性.所得结论是时滞无关的,即绝对稳定性充分条件仅依赖于时滞导数的大小,特别地,时滞可为无界函数.通过一个示例说明有时得到时滞相关的绝对稳定性条件比时滞无关的稳定性条件具有更大的保守性,促使今后寻找另外的方法和工具得到保守性较低的稳定性条件.仿真示例同时说明此方法对时滞为无界函数时的有效性.

Absolute Stability for Lurie Control Systems with Time-varying Delay

The absolute stability for Lurie type direct control systems and indirect control systems with several time-varying delays is discussed respectively. Based on Lyapunov stability theory and linear matrix inequalities, absolute stability criteria are derived. The result depends on the size of delay derivative and the delays can be unbound functions. Finally, an example shows that the delay-dependent absolute stability condition is more conservative than the deLay-independent one sometimes, Other methods and tools are needed to solve this problems, Simulation example indicates the effectiveness of the proposed approach simultaneity.