Robust stability of sampled-data control systems with uncertain time-delays
时滞不确定采样控制系统的鲁棒稳定性

We propose a quantitative method for analyzing the robust stability of sampled-data systems with uncertain time-delays. Because the sampled-data systems are obtained from continuous-time systems by sampling, the time-delay in the sampled-data system must also be treated in the continuous-time system. It is pointed out that a stable sampled-data system with a time-delay equal to the integer-multiple of the sampling period may be destabilized by a small continuous time-delay. A new variable w(t) is defined to describe the dynamic response caused by the uncertain continuous timedelay. The feedback loop of w(t) is then divided into two parts. One depends on the uncertain time-delay, and the other is independent of the time-delay. A special frequency response method is proposed to determine the existence of the periodic solution of the system caused by the uncertain time-delay. The graphic-analytical solution is then verified by the modified z-transform method and by simulation. The proposed method can also be used for robust stability analysis of continuous-time systems with time-delays.