Input-to-state Stability Of Numerical Methods For Control Systems With Delays

Control systems often appear in many fields of technology,such as chemistry, machinery,electronic engineering,physics,medicine,etc.Based on the practica-bility of control systems,the stability is an important component of the theory study.Many scholars have done a lot of work,and a great deal of results have been found.Since Sontag proposed the IS-Stability of Control Systems in 1980s,Sontagself(1996), Wang and Jing(2001),Hu and Liu(2006),Yu et.al.(2008) have done a lot of researches in the field,but what they studied were only limited to the control systems without delays.However,in practice,there axe many delay phenomena in control systems inevitably.Therefore,it is necessary to extend their work further to the control systems with delays.In the present thesis,we focus on the IS-stability of numerical methods for the control systems with delays.The main results obtained are as follows:(1)The sufficient condition for IS-stability of linear control system are derived. Then the IS-stability of Runge-Kutta methods and linearθ-methods for linear control systems with delays are investigated,and several numerical tests are given that confirm the theoretical results.(2) We provide some sufficient conditions for IS-stability of nonlinear control systems.On base of the conditous,we have studied the IS-stability of Runge-Kutta methods and one-leg methods.Some numerical tests are processed to verify the theoretical results.It should be pointed out that when the results obtained in this paper are applied to the control systems without delays,they are accordant with those in the existing literature,thus they are more general.