Stability Analysis And Control For Time Delay Systems Based On Integral Inequalities

Time delay phenomena(delay in time)extensively exist in practical engineering systems.The existence of time delay is the main source to yield system performance degradation or instability of system,and brings difficulties in stability analysis and controller design for systems.Therefore,the research on time delay systems is of great significance for practical values and theoretical meanings.In this dissertation,based on Lyapunov stability theory,several delay-dependent performance analysis and controller design problems for time delay systems and networked control systems are investigated via multiple integral forms of augmented Lyapunov-Krasovskii(L-K)functionals and improved integral inequalities without introducing additional computational complexity.The main contributions of this dissertation are presented as follows:1.The stability analysis and robust control for interval time delay system are discussed.Firstly,the Wirtinger-based double and triple integral inequalities are developed for time-varying delay case.Then,by constructing quadruple integral form of L-K functional,two types of delay-dependent stability conditions with less conservatism are derived for the continuous and differential delay and the continuous but not differential one by using the obtained inequalities to handle the integrals,respectively.Meanwhile,the relationship between the two types of stability criteria is also constructed theoretically.Based on the characteristics of constant delay,the stability condition for constant delay system is achieved by rational modification for L-K functioanl.On the other hand,the derived conditions are extended to the robust stability analysis and robust control for systems with time-varying structure uncertainties.2.The stability analysis and stabilization for networked control system are investigated.Firstly,the model of networked control system with network-induced delay and data packet dropout is established by the input delay approach.Then,a new delay partitioning approach is proposed,which divides the delay interval into two variable subintervals.Different multiple integral types of L-K functionals are constructed,and the information on delay and packet dropout is taken into consideration,respectively,and less conservative stability criterion is obtained.For the case with large delay lower bound,improved stability conditon is achieved by dividing the lower bound into multiple equal-distant parts,which considers more information on the lower bound.The derived stability criterion is extended to stabilization problem for networked control systems.3.The H_? performance analysis and H_? control problem for time delay systems with external disturbance are studied.Firstly,more general model of time delay system with state delay or input delay is established.Then,based on the recently introduced auxiliary function-based integral inequality,improved triple integral inequality is proposed,which will further reduce the estimation gap during the bounding process for integral terms and utilize the information on the triple integrals of system state.By constructing quadruple integral type of L-K fuctional,the H_? performance criterion with less conservatism for two types of time delay systems are derived.The derived condition is also extended to H_? controller design approach.4.The stability analysis for a type of delayed neural networks is investigated.Firstly,by establishing two types of polynomials,the double integral inequalities in form of infinite series are developed without introducing additional matrix variables,the estimation values of which are more and more accurate with the growth of the degrees of the intermediate polynomials.Then,the triple integral type of augmented L-K functional is constructed,and the activation function-based term takes more information of delay and information on slope of activation function into consideration.Under more general activation function condition,less conservative stability conditions of delayed neural networks for the continuous and differential delay and the continuous but not differential one are established by utilizing equations with various delay information.5.The mixed H_? and passivity-based control for networked cascade control systems is investigated.Firstly,more general model of networked cascade control system with network phenomena in both primary and secondary closed-loops is constructed by input delay approach.By utilizing a new performance index and constructing triple integral form of L-K functional,the information on network phenomena of dual loops are taken into full consideration,and the mixed H_? and passivity-based performance analysis cirterion for networked cascade control system is obtained.The derived condition is extended to mixed H_? and passivity-based controller design approach.