Study On Delay-Dependent Robust Stabilization For A Class Of Uncertain Neutral Systems

Different from the retarded system,which contains delays only in its states,the neutral one contains delays not only in its states but also in the derivatives of its states.In the previous neutral systems,both of the time-delays are constants (time-unvarying) and they are equal.With the further research,systems become more and more complicated.For instance,both are unequal constants;one is time-unvarying and the other is time-varying,etc.This paper studied the relatively complex neutral system at present - the uncertain neutral system with mixed time-varying delays.Just as its name implies, both of the delays are time-varying ones,and not unequal.If we let the two time-varying delays equal to different constants(or the same constant),or let either of the time-delays equal to a constant,the system in this paper is the same as that in previous references.That is,the conclusions of this paper contain the past ones.Augmented Lyapunov functional including triple integral was chosen in this paper.It was further improved,compared with the ones appearing in other thesis,on which neutral systems were investigated.On the other hand,free-weighting matrices were utilized to found several new criteria.The results show that the novel method is less conservative than some existing ones.As for the problem of designing the state feedback H_∞controller,it is difficult to work out the controller if we pre- and post-multiply LMI by a certain diagonal matrix and its transposition,which leads to the emergence of many new nonlinear matrices.Thus,a new strategy was applied to cope with it.The terms including K or K~T were moved out of the biggest matrix,firstly.And then,a special term was added. At last,we used Schur complement to obtain the theorems.It was easy to calculate the feedback control gain by the LMI toolbox of MATLAB. Designing controller was also involved in the guaranteed cost control.The approach was the same as that of designing state feedback H_∞controller.Therefore, the novel method is applicable to other systems as well as other controllers' design.In order to illustrate the effectiveness and the merits of the main results,a few numerical examples were employed to demonstrate the feasibility of the stability conditions,seek the upper bounds on the delays,solve the minimum value of H_∞norm constraint,design the state feedback H_∞controller and guaranteed cost controller,respectively.