Research And Its Application Of The Stability Of Time-varying Delays System Based On General Integral Inequalities

As the revolution of human society,people have higher demands for performance indicators of systems with time-varying delay.In the most of influence factors,time delay is an important factor that causes of system instability.On the one hand,many results in the study of systems with constant time delay are exited,and the systems with time-varying delay are worth further exploring.Therefore,it is necessary to explore the stability of systems which contain double or even more time-varying delays.On the other hand,bilateral teleoperation system has become a convenient tool in recent years.It is worth delving how to decrease the influence of time delay on the performance of bilateral teleoperation.And the stability of time-varying delays systems and its application are studied in this paper:1)For a linear system with two additive time-varying delays,the stability problem is discussed.Firstly,an appropriate Lyapunov-Krasovskii functional(LKF)is constituted,which contains the first-order derivative integral terms related to the system.The derivative of LKF is carried out along the system,and the integral terms existing in the derivative function are estimated adopting the Wirtinger-based integral inequality and the generalized reciprocally convex matrix inequality.Secondly,with the help of linear matrix inequality(LMI)toolbox,the delay-dependent stability scheme is achieved.The results show that the maximum allowable upper bound of time delays is improved and the number of decision variables is cut down.In addition,the obtained stability criterion is less conservative.Bitter end,MATLAB simulation proves that the strategy is effective.2)A stability criterion for time-varying delays systems on account of the second derivative integral inequality is offered.First,an augmented LKF consists of double and triple integral terms with second derivatives.Next,the derivation of LKF is estimated pass through applying the perfected free-matrix-based integral inequality and reciprocally convex combination lemma.A less conservative delay-dependent asymptotic stability criterion is obtained.At length,MATLAB simulation is used to verify the effectiveness of the proposed criterion.3)A time-delay dependent exponential stability condition is established for the stability of a master-slave bilateral teleoperation system.At first,a passive control strategy based on proportional differential position-position(PD-PP)is proposed.Secondly,a new LKF is constructed by means of exploiting the relevant information of the teleoperation system.Moreover,the derivative of LKF is estimated via employing the general integral inequality and the extended reciprocally matrix inequality.In the framework of LMI,a less conservative delay-dependent exponential stability condition is given,which proposes a larger maximum allowable upper bound.Ultimately,the success of the control tactics is confirmed by MATLAB simulation conclusion.