Stabilization Of A Class Of Wave Systems With Combined Time-delay Boundary Control

The string vibration system can be used to solve practical problems in control engineering.Therefore,the study of string vibration systems with time-boundary control has important theoretical value and practical significance.This paper mainly studies the stability of the combined delay boundary control system with damping coefficient.By introducing a linear transformation,the system is converted into an undamped system,and a simple spectral analysis is performed on the system.The existence of the system basis is proved,and the system meets the spectral determined growth conditions.On the premise of the relationship between position and stability,the spectral point position of the system is discussed in detail.It is obtaned that t e system is exponentlly stahe when comining coeficients ??1/2,and the system is unstable at the time of ?<1/2.Finally,the stability of the system and other systems is compared,it is found that the existence of weight coefficients ? and damping coefficients a causes some changes in the stability of the system.