We study stochastically blinking dynamical systems as in the companion paper (Part I). We analyze the asymptotic properties of the blinking system as time goes to infinity. The trajectories of the averaged and blinking system cannot stick together forever, but the trajectories of the blinking system may converge to an attractor of the averaged system. There are four distinct classes of blinking...

This paper investigates the controller synthesis of uncertain linear time-delay systems. Stabilizability criteria are derived based on a discretized Lyapunov functional approach. A new controller design method is developed. Numerical examples show that the results using the proposed method are less conservative than some existing ones.

A delayed periodic n-species simple food-chain system with Holling type-II functional response is investigated. By means of Gaines and Mawhin’s continuation theorem of coincidence degree theory and by constructing appropriate Lyapunov functionals, sufficient conditions are obtained for the existence and global attractivity of positive periodic solutions of the system.

In this paper, an entropy based associative memory model will be proposed and applied to memory retrievals with an orthogonal learning model to compare with the conventional model based on the quadratic Lyapunov functional to be minimized during the retrieval process. In the present approach, the updating dynamics will be constructed on the basis of the entropy minimization strategy which may b...

We present a dual form of Lyapunov-Krasovskii functional which allows the problem of controller synthesis of multi-delay systems to be formulated and solved in a convex manner. First, we give a generalized version of the dual stability condition formulated in terms of Lyapunov operators which are positive, self-adjoint and preserve the structure of the statespace. Second, we provide a class of ...

This note considers the problem of stability analysis of discrete–time homogeneous dynamics, i.e., positively homogeneous of the first degree dynamics. An example of a homogeneous and even continuous dynamics that is globally exponentially stable and that does not admit any λ–contractive proper C–set is presented. This motivates us to propose a natural generalization of this concept, namely, (k...

Recently, the population dynamic systems with impulsive controls have been researched by many authors. However, most of them are reluctant to study the seasonal effects on prey. Thus, in this paper, an impulsively controlled two-prey one-predator system with the Beddington-DeAngelis type functional response and seasonal effects is investigated. By using the Floquet theory, the sufficient condit...

A mathematical driver model is given in the spacial equation form, which takes into account the previewed information of the path. Optimal control method is considered for the ideal no time-delay case and Lyapunov-Krasovskii functional approach is applied to deal with drivers’ reaction time-delay. For both cases, exponential stability is guaranteed for the closedloop system.

We establish some new sufficient conditions to the uniform asymptotically stability and boundedness of the solutions for a kind of non-autonomous differential equations of third order with constant delay. By defining an appropriate Lyapunov functional, we prove two new theorems on the subject. Our results improve and form a complement to some known recent results in the literature.

Here, a predator-prey model with Hassell-Varley type functional responses is studied. Some sufficient conditions are obtained for the permanence and global asymptotic stability of the system by using comparison theorem and constructing a suitable Lyapunov functional. Moreover, an example is illustrated to verify the results by simulation.