The stability and stabilization of a class of nonlinear discrete time delayed systems(NDTDS) with time-varying delay and norm-bounded nonlinearity are investigated. Based on discrete time Lyapunov–Krasovskii function...The stability and stabilization of a class of nonlinear discrete time delayed systems(NDTDS) with time-varying delay and norm-bounded nonlinearity are investigated. Based on discrete time Lyapunov–Krasovskii functional method, a sufficient delaydependent condition for asymptotic stability of nonlinear systems is offered. Then, this condition is used to design a new efficient delayed state feedback controller(DSFC) for stabilization of such systems. These conditions are in the linear matrix inequality(LMI) framework. Illustrative examples confirm the improvement of the proposed approach over the similar cases. Furthermore, the obtained stability and stabilization conditions will be extended to uncertain discrete time delayed systems(UDTDS) with polytopic parameter uncertainties and also with norm-bounded parameter uncertainties.展开更多
We studied the response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control using the stochastic averaging method. First, the time-delayed feedback bang-ba...We studied the response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control using the stochastic averaging method. First, the time-delayed feedback bang-bang control force is expressed approximately in terms of the system state variables without time delay. Then the averaged It6 stochastic differential equations for the system are derived using the stochastic averaging method. Finally, the response of the system is obtained by solving the Fokker-Plank-Kolmogorov （FPK） equation associated with the averaged lt6 equations. A Duffing oscillator with time-delayed feedback bang-bang control under combined harmonic and white noise excitations is taken as an example to illus- trate the proposed method. The analytical results are confirmed by digital simulation. We found that the time delay in feedback bang-bang control will deteriorate the control effectiveness and cause bifurcation of stochastic jump of Duffing oscillator.展开更多
In this paper, a delayed SEIRS epidemic model with nonlinear incidence rate and impul- sive vaccination is investigated. In vaccination strategy, we perform impulsive vaccina- tion of newborn infants. Using the discre...In this paper, a delayed SEIRS epidemic model with nonlinear incidence rate and impul- sive vaccination is investigated. In vaccination strategy, we perform impulsive vaccina- tion of newborn infants. Using the discrete dynamic system determined by stroboscopic map, we obtain an infection-free periodic solution and establish conditions, on which the solution is globally attractive. We also conclude that the disease is permanent if the parameters of the model satisfy appropriate conditions. Finally, we illustrate the effec- tiveness of our theorems with numerical simulation. The results obtained in this paper are a good extension of the results obtained in [J. Hou and Z. Teng, Continuous and impulsive vaccination of SEIR epidemic models with saturation incidence rate, Math. Comput, Simulat. 79 （2009） 3038 3054] to the corresponding delayed SEIRS epidemic model with nonlinear incidence rate and impulsive vaccination.展开更多
文摘The stability and stabilization of a class of nonlinear discrete time delayed systems(NDTDS) with time-varying delay and norm-bounded nonlinearity are investigated. Based on discrete time Lyapunov–Krasovskii functional method, a sufficient delaydependent condition for asymptotic stability of nonlinear systems is offered. Then, this condition is used to design a new efficient delayed state feedback controller(DSFC) for stabilization of such systems. These conditions are in the linear matrix inequality(LMI) framework. Illustrative examples confirm the improvement of the proposed approach over the similar cases. Furthermore, the obtained stability and stabilization conditions will be extended to uncertain discrete time delayed systems(UDTDS) with polytopic parameter uncertainties and also with norm-bounded parameter uncertainties.
基金Project supported by the National Natural Science Foundation of China(Nos.10772159 and 10802030)the Research Fund for Doctoral Program of Higher Education of China(No.20060335125)
文摘We studied the response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control using the stochastic averaging method. First, the time-delayed feedback bang-bang control force is expressed approximately in terms of the system state variables without time delay. Then the averaged It6 stochastic differential equations for the system are derived using the stochastic averaging method. Finally, the response of the system is obtained by solving the Fokker-Plank-Kolmogorov （FPK） equation associated with the averaged lt6 equations. A Duffing oscillator with time-delayed feedback bang-bang control under combined harmonic and white noise excitations is taken as an example to illus- trate the proposed method. The analytical results are confirmed by digital simulation. We found that the time delay in feedback bang-bang control will deteriorate the control effectiveness and cause bifurcation of stochastic jump of Duffing oscillator.
基金This work is supported by the National Natural Science Foundation of China under Grant 61174039. The authors would like to thank the editor and reviewers for their hard work to the improvement of the quality of this paper.
文摘In this paper, a delayed SEIRS epidemic model with nonlinear incidence rate and impul- sive vaccination is investigated. In vaccination strategy, we perform impulsive vaccina- tion of newborn infants. Using the discrete dynamic system determined by stroboscopic map, we obtain an infection-free periodic solution and establish conditions, on which the solution is globally attractive. We also conclude that the disease is permanent if the parameters of the model satisfy appropriate conditions. Finally, we illustrate the effec- tiveness of our theorems with numerical simulation. The results obtained in this paper are a good extension of the results obtained in [J. Hou and Z. Teng, Continuous and impulsive vaccination of SEIR epidemic models with saturation incidence rate, Math. Comput, Simulat. 79 （2009） 3038 3054] to the corresponding delayed SEIRS epidemic model with nonlinear incidence rate and impulsive vaccination.
