Chunxia Fan

Stability switches and Hopf bifurcations of an isolated population model with delay-dependent parameters

The dynamical behaviors of an isolated population model involving delay-dependent parameters are investigated. It is shown that the positive equilibrium switches from being stable to unstable and then back to stable as the delay increases, and the Hopf bifurcation occurs finite times between the two critical values of stability changes which can be analytically determined. Moreover, the bifurcating periodic solutions are expressed analytically in an approximate form by the perturbation approach and Floquet technique. The direction and stability of the bifurcating periodic solutions are also determined. Finally, the validity of the results is shown by the consistency with the numerical simulations.

Fault-tolerant synchronization of complex dynamical networks with actuator faults

This paper presents the fault-tolerant synchronization controller design for a class of complex dynamical networks (CDNs) in the presence of actuator being partial faulting. By using the prior knowledge of the actuator faults, the complex network with actuator faults is described as a complex network with parameter uncertainties. Furthermore, a fault tolerant synchronization criterion in the form of linear matrix inequality is proposed on the basis of the Lyapunov stability theorem and Schur complement lemma. Finally, a numerical simulation is carried out to demonstrate the effectiveness of the proposed fault-tolerant synchronization controller.

Decentralized Control for Large-Scale Systems with Uncertain Missing Measurements Probabilities

For large-scale systems which are modeled as interconnection of networked control systems with uncertain missing measurements probabilities, a decentralized state feedback controller design is considered in this paper. The occurrence of missing measurements is assumed to be a Bernoulli random binary switching sequence with an unknown conditional probability distribution in an interval. A state feedback controller is designed in terms of linear matrix inequalities to make closed-loop system exponentially mean square stable and a prescribed performance is guaranteed. Sufficient conditions are derived for the existence of such controller. A numerical example is also provided to demonstrate the validity of the proposed design approach.