Research On Time Delay Stability For Lur'e Systems

Lur'e system is a representative nonlinear system and time delay is a common phenomenon.Time delays is the sources of instability,and poor performance of the dynamical systems.Therefore,it is of theoretical significance and practical value to study the time delays related stability of Lur'e system.In this paper,general Lur'e systems,neutral Lur'e systems and discrete Lur'e systems is studied by employing Lyapunov-Krasovskii functional approach.The main results are as follows:1.For stability of time-delay general Lur'e system,our treatment is as follows: Firstly,a novel relaxed condition of L-K functional is proposed.Secondly,by deriving for L-K functional,simplifying derivation of L-K functional and combining some inequality techniques such as integral inequality and reciprocally convex approach,a stability criterion of general Lur'e system are derived in terms of LMIs.Finally,by compering simulation results with previous,this criterion is more effective.2.For stability of time-delay neutral Lur'e system,two criteria with less conservatism are obtained by employing two different methods in this paper.First method: we propose a novel nonlinear decomposition approach.Then,by employing L-K functional approach combining with inequality techniques,we can derive a stability criterion of neutral Lur'e system.The criterion has less conservatism than previous from comparison of simulation result.Second method: firstly,we proposed a improved double integral inequality.Secondly,by constructing a new augmented L-K functional and combining the proposed double integral inequality,a stability criterion can be derived.Finally,by comparing with the existing references,the criterion is less conservative.3.For stability of time-delay discrete Lur'e system,our treatment is as follows: First,an augmented L-K functional which can take into account the more nonlinear factors is proposed.Secondly,by deriving the L-K functional,simplifying derivation of L-K functional and combining Jenson's summation inequality,Jenson's double summation inequality and other inequalities,a stability criterion for discrete Lur'e system is derived in terms of LMIs.Finally,the simulation results show that the criterion has less conservatism compared with the existingpaper.