The stability analysis and planning for multivariable linear time-delay systems and its application

Based on Lyapunov´s theory of stability, analysis on a control process of oil-water separation with time-delay, coupling and uncertainty in the unite station, is presented in this paper. An equation of sufficient condition for multi-variable linear delayed systems with delayed independent stabilization is derived and another forms are also given. Based on this, several simple criterions for judging independent stabilization from linear delayed system are presented. We also discuss the exponential stability for delayed system and also provide the sufficient condition of exponential stability with any appointed convergent rate and its corresponding deductions. Using these conditions, we can choose a set of suitable parameters to reduce the conservation. By calculating and being compared with methods of the literature, the results show that our methods have less conservation.