Stability Analysis For Time-delay Systems And Complex Dynamical Networks

The system often oscillates because of the existence of time delay,and its performance will deteriorate or even be unstable,so it is of great practical significance to analyze the stability of the time-delay system.The stability and controller design of time-varying delay system and complex dynamical network system with time-delay have been concerned by many scholars and become a hot topic in the field of control.The contents of this paper are as follows:1?The problem of time delay dependent stability analysis for time-varying delay systems is discussed.On the one hand,based on the free matrix inequality,the relax condition of the positive definite constraint of the partial matrix in the Lyapunov-Krasovskii(L-K)functional is obtained.On the other hand,the stability criterion of the system is obtained by the second-order Bessel-Legendre inequality,the free matrix inequality to deal with the integral term after L-K functional derivation and adding a constant equal to zero.Finally,the results of numerical examples show that this method is less conservative.2?The stability analysis and sampled-data controller design of complex dynamical network system with time-varying delays are discussed.Firstly,we constructed a new L-K functional for a given time-varying delay complex dynamical network model,which introduced the correlation matrix of data sampling interval and optimized the double-closed loop functional and made full use of the state information of the system.A new criterion for stability is obtained by using some newly reported integral inequalities to estimate the derivative of the constructed L-K functional.Then a sampled-data controller is designed for complex dynamical networks model with three nodes and six nodes.Finally,the less conservative and feasibility of this method are proved by numerical examples and state trajectories.