Local Stabilization Problem For Systems With Input Saturation And Time Delay

It was common that saturation and delay in actual systems,which were the main factor of the control effect.The systems which contain input saturation or time delay had been researched for plenty of works for decades.The systems which contain both input saturation and time delay were especially hard to process,so the research of these systems was valuable.This paper major in the stabilization of unstable systems,and we came up to 4 methods for the systems stability criterion.First of all,we studied the unstable system with input saturation,and introduced the convex hull description method.Based on this convex hull description,we advanced a new method to decrease the conservation of the attraction domain estimate by increase numbers of the decision vector.Then,we proposed 2 stability criterions for the system with input saturation and timedelay via Razumikhin theorem.One was based on Jessen inequality,the other was based on system deformation.Last,we proposed 2 stability criterions for the system with input saturation and timedelay via Krasovskii theorem.One was based on Krasovskii-function with derivative of the states,the other was based on Krasovskii-function without that.Moreover we compared the simulation results of the 4 theorem.What had introduced in this paper were very valuable for the local stabilization of the systems with input saturation and input time-delay,the estimate of the attraction domain.The feasibility of the 4 theorems had been verified via numerical simulations.