Asymmetric Functional Method For Stability Of Time-delay System

Time delay phenomenon widely exists in various practical systems,such as network transmission system,communication system,power system and so on.Time delay tends to negatively impact the performance of dynamical systems but are unavoidable.The study on time-delay systems has important theoretical significance and application value,especially for fundamental stability problems.For time-delay systems,whether it is the improvement of basic stability methods,or the in-depth analysis and control of complex systems,they are all important problems to be solved urgently.Therefore,this thesis mainly studies the stability and stabilization of linear time-delay systems,T-S fuzzy time-delay systems,and sampled data control systems,and proposes a new asymmetric L-K functional method for time-delay systems,combines the methods with various improved techniques to obtain a series of results in the form of linear matrix inequality with low conservatism.The main research work and results of this thesis are summarized as follows:1.For the stability of linear time-delay systems,a new asymmetric L-K functional method is proposed,which improves the traditional symmetric functional method.The new functional no longer requires the involved matrices to be all symmetric and positive definite.According to the new method,a series of time-delay-dependent asymptotic stability results are obtained,which are less conservative than previous results.Finally,numerical examples are used to fully compare the obtained results with those in the literature to verify the effectiveness of the new method and its superiority over traditional methods.2.Based on the proposed asymmetric L-K functional method,the stability and stabilization of T-S fuzzy time-delay systems are studied,including two cases of constant time delay and time-varying time delay.According to the new method combined with the improved membership-function-dependent approach,the conservativeness of the stability and stabilization results are effectively reduced,and the results are significantly improved compared with the previous results.And several numerical examples are provided to demonstrate the effect of the method and results and the superiority compared with the literature.3.The stability and stabilization of sampled-data systems are studied,which is divied in two parts.In the first part,for the stability of sampled-data systems,a novel semi-loopedfunctional method is proposed,which effectively improves and extends the previous common methods,and leads to a series of low-conservative stability criteria.The second part is for the T-S fuzzy systems under sampled-data control.Based on the semi-loopedfunctional method,combined with the proposed asymmetric time-delay functional term and the sampling-interval-dependent functional term,the stability criterion of the systems with time delay is obtained.And to fully demonstrate and compare the new method,the stability criterion of the systems without time delay is provided,then the corresponding control stabilization results are obtained,where the proposed stabilization simplification technique is combined.These results are less conservative than previous results.Some examples are provided at the end of both parts to show the effect and advantages of the results.