In this paper, the stabilizability problem for chaotic discrete-time systems under the generalized delayed feedback control (GDFC) is addressed. It is proved that 0 < det(I − A) < 2 is a necessary and sufficient condition of stabilizability via m-step GDFC for an n-order system with Jacobi A. The condition reveals the limitation of GDFC more exactly than the odd number limitation. An analytical...

Time delay is a common phenomenon in robotic systems due to computational requirements and communication properties between or within high-level and low-level controllers as well as the physical constraints of the actuator and sensor. It is widely believed that delays are harmful for robotic systems in terms of stability and performance; however, we propose a different view that the time delay ...

We investigate the phenomenon of noise-enhanced phase synchronization (PS) in coupled time-delay systems, which usually exhibit non-phase-coherent attractors with complex topological properties. As a delay system is essentially an infinite dimensional in nature with multiple characteristic time scales, it is interesting and crucial to understand the interplay of noise and the time scales in ach...

In this paper, we obtain an analytical Lyapunovbased stability conditions for scalar linear and nonlinear stochastic systems with discrete time-delay. The Lyapunov– Krasovskii and Lyapunov–Razumikhin methods are applied with techniques from stochastic calculus to obtain the regions of mean square asymptotic stability in the parameter space. Both delay-independent and delay-dependent stability c...

In this paper, we consider the projective-anticipating, projective, and projective-lag synchronization in a unified coupled time-delay system via nonlinear observer design. A new sufficient condition for generalized projective synchronization is derived analytically with the help of Krasovskii-Lyapunov theory for constant and variable time-delay systems. The analytical treatment can give stable...

This paper examines the problems of robust H∞ filtering design for linear parameter-varying discrete-time systems with time-varying state delay. We present new H∞ performance criteria that depend on the parameters and the delay-varying magnitude using appropriately selected Lyapunov-Krasovskii functional. Then the corresponding filter can be obtained from the solution of convex optimization pro...

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We study generalized variable projective synchronization between two unified time delayed systems with constant and modulated time delays. A novel Krasovskii-Lyapunov functional is constructed and a generalized sufficient condition for synchronization is derived analytically using the Lyapunov stability theory and adaptive techniques. The proposed scheme is valid for a system of n-numbers of fi...

A methodology is proposed for the control of switching systems characterized by linear system dynamics with a time delay in the input channel. The method incorporates a state predictor that at each switching period determines the effect that the next control input will have on the future output of the system, and chooses the input that will take the system closest to the desired future state. T...

We present a technique for bounded invariant verification of nonlinear networked dynamical systems with delayed interconnections. The underlying problem in precise boundedtime verification lieswith computing bounds on the sensitivity of trajectories (or solutions) to changes in initial states and inputs of the system. For large networks, computing this sensitivity with precision guarantees is c...