In this paper, the Lotka-Volterra competition system with discrete and distributed time delays is considered. By analyzing the characteristic equation of the linearized system, the local asymptotic stability of the po...In this paper, the Lotka-Volterra competition system with discrete and distributed time delays is considered. By analyzing the characteristic equation of the linearized system, the local asymptotic stability of the positive equilibrium is investigated. Moreover, we discover the delays don＇t effect the stability of the equilibrium in the delay system. Finally, we can conclude that the positive equilibrium is global asymptotically stable in the delay system.展开更多
This paper is concerned with the problem of observer-based fuzzy control design for discrete-time T-S fuzzy bilinear stochastic systems with infinite-distributed delays. Based on the piecewise quadratic Lyapunov funct...This paper is concerned with the problem of observer-based fuzzy control design for discrete-time T-S fuzzy bilinear stochastic systems with infinite-distributed delays. Based on the piecewise quadratic Lyapunov functional （PQLF）, the fuzzy observer-basedcontrollers are designed for T-S fuzzy bilinear stochastic systems. It is shown that the stability in the mean square for discrete T-S fuzzy bilinear stochastic systems can be established if there exists a set of PQLF can be constructed and the fuzzy observer-based controller can be obtained by solving a set of nonlinear minimization problem involving linear matrix inequalities （LMIs） constraints. An iterative algorithm making use of sequential linear programming matrix method （SLPMM） to derive a single-step LMI condition for fuzzy observer-based control design. Finally, an illustrative example is provided to demonstrate the effectiveness of the results proposed in this paper.展开更多
In this paper, the exponential stability analysis for ODE switched systems with time delay is extended to distributed parameter switched systems(DPSS) in Hilbert space. For a given family of exponential stable subsyst...In this paper, the exponential stability analysis for ODE switched systems with time delay is extended to distributed parameter switched systems(DPSS) in Hilbert space. For a given family of exponential stable subsystems, this paper focuses on finding conditions to guarantee the overall DPSS' exponential stability. Based on semigroup theory, by applying piecewise Lyapunov-Krasovskii functionals method incorporated average dwell time approach, sufficient conditions for exponential stability are derived. These conditions are given in the form of linear operator inequalities(LOIs)where the decision variables are operators in Hilbert space, and the stability properties depend on switching rule. Being applied to heat switched propagation equations, these LOIs are reduced to standard Linear Matrix Inequalities(LMIs). Finally, a numerical example is given to illustrate the effectiveness of the proposed result.展开更多
基金the Education Foundation of Henan Province(07110005)
文摘In this paper, the Lotka-Volterra competition system with discrete and distributed time delays is considered. By analyzing the characteristic equation of the linearized system, the local asymptotic stability of the positive equilibrium is investigated. Moreover, we discover the delays don＇t effect the stability of the equilibrium in the delay system. Finally, we can conclude that the positive equilibrium is global asymptotically stable in the delay system.
文摘This paper is concerned with the problem of observer-based fuzzy control design for discrete-time T-S fuzzy bilinear stochastic systems with infinite-distributed delays. Based on the piecewise quadratic Lyapunov functional （PQLF）, the fuzzy observer-basedcontrollers are designed for T-S fuzzy bilinear stochastic systems. It is shown that the stability in the mean square for discrete T-S fuzzy bilinear stochastic systems can be established if there exists a set of PQLF can be constructed and the fuzzy observer-based controller can be obtained by solving a set of nonlinear minimization problem involving linear matrix inequalities （LMIs） constraints. An iterative algorithm making use of sequential linear programming matrix method （SLPMM） to derive a single-step LMI condition for fuzzy observer-based control design. Finally, an illustrative example is provided to demonstrate the effectiveness of the results proposed in this paper.
基金supported by the National Natural Science Foundation of China under Grant Nos.61273119,61104068,61374038the Natural Science Foundation of Jiangsu Province of China under Grant No.BK2011253
文摘In this paper, the exponential stability analysis for ODE switched systems with time delay is extended to distributed parameter switched systems(DPSS) in Hilbert space. For a given family of exponential stable subsystems, this paper focuses on finding conditions to guarantee the overall DPSS' exponential stability. Based on semigroup theory, by applying piecewise Lyapunov-Krasovskii functionals method incorporated average dwell time approach, sufficient conditions for exponential stability are derived. These conditions are given in the form of linear operator inequalities(LOIs)where the decision variables are operators in Hilbert space, and the stability properties depend on switching rule. Being applied to heat switched propagation equations, these LOIs are reduced to standard Linear Matrix Inequalities(LMIs). Finally, a numerical example is given to illustrate the effectiveness of the proposed result.
