Robust Control Of Two Types Of Lower Trigonometric Delay Systems

There are many engineering applications with delay,such as master-slave robot,neural systems,chemical and biological systems.Because of delay,the modeling,analysis and control of systems become increasingly difficult,it was declined the performance of the control system,and even lead to system instability.Therefore,the study of delay systems becomes more important and meaningful.In this paper,we deeply research the lower triangular system that has unknown time-varying delays in both states and input,the uncertain nonlinear system with unknown time-varying input delay and additive disturbances of these two types of delay systems.The lower triangular system is the most typical dynamical system;but the nonlinear is the most common phenomenon of nature and engineering technology.Therefore,it is more appropriate to construct the nonlinear system in many practical production and living engineering systems.The main research of this paper are as follows:(1)For the lower triangular system,it has unknown time-varying delays in both states and input,this paper only provides delay which is bounded,but the boundary and the time-varying rate are unknown.First,this paper proposes a new adaptive output feedback controller.Then,in order to deal with unknown time-varying delay,this paper gives a new transformation and technology.Finally,this paper obtains the output feedback controller globally regulates the system.A simulation example illustrates that the design of output feedback control is feasible.(2)For the uncertain nonlinear system with unknown time-varying input delay,the main purpose of this artical is to design a tracking controller for it.First,by using the past states in a finite integral over a constant estimated delay interval,a novel filtered error signal is designed.In this paper,the maximum tolerance error is required to be between the unknown time delay and the constant estimation of a time delay to ensure that the tracking error of the design is uniformly bounded to zero.Then,the controller develop-ment is based on an approach which using Lyapunov-Krasovskii functionals to analyze the effects of unknown sufficiently slowly time-varying input delays.Finally,in order to prove ultimate boundedness of the tracking error signals,this paper provides a stability analysis.Numerical simulation results illustrate the performance of the developed robust controller.