Absolute Stability Analysis Of Delayed Lur’e Control Systems

Time-delay phenomenon widely exists in a variety of practical systems,and Lur’e control system is a very typical nonlinear control system.Therefore,the absolute stability of Lur’e systems with time-delay has been widely concerned by many researchers.To begin with,the delayed Lur’e system is introduced in this paper,and the significance of the delayed Lur’e system and the methods of absolute stability are summarized.Furthermore,the preparation knowledge including some based concepts,theories,lemmas and notations are presented,then,this paper discusses the problems of the absolute stability of a class of delayed Lur’e systems and the neutral-type Lur’e system with time-varying delay.Finally,it shows the conclusion and prospect,which concludes the summaries and further research of this work.The main contributions in this work are as follows:1.About absolute stability criteria of delayed Lur’e system:Some appropriate Lyapunov-Krasovskii functionals(LKFs)are constructed firstly;The absolute stability criteria of the delayed Lur’e systems are derived in the form of linear matrix inequalities(LMIs)by using Kim integral inequality to estimate the upper bound of the derivative of the LKFs;Finally,two numerical examples are included to illustrate the effectiveness and the improvement of the proposed method and less conservative than relative references.2.About absolute stability criteria of neutral-type Lur’e system with timevarying delay:The variation interval of delay is divided into two unequal parts,then some appropriate LKFs are constructed in each of the sub-intervals;The absolute stability criteria of the delayed Lur’e systems are derived in terms of the LMIs by using the reciprocally convex technique and integral inequality method to estimate the upper bound of the derivative of the LKFs;The advantage of the obtained criteria lies in that more information of the time delays can be obtained by selecting the values of the delay decomposition parameter.Finally,a numerical example is given to illustrate the improved method in the paper can effectively reduce the conservativeness.