Motivated by the fact that delay difference inclusions (DDIs) form a rich modeling class that includes, for example, uncertain time-delay systems and certain types of networked control systems, this paper provides a comprehensive collection of Lyapunov methods for DDIs. Firstly, the Lyapunov-Krasovskii approach, which is an extension of the classical Lyapunov theory to time-delay systems, is co...

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...

| The problem of synchronization of coupled chaotic systems is considered. The notion of local transversal Lyapunov exponents is introduced. We show that they can be successfully used in investigations of the synchronization properties. The technique is illustrated with computer simulations.

In this paper, a generalized synchronization scheme, which is called function synchronization, for chaotic systems is studied. Based on Lyapunov method and active control method, we design the synchronization controller for the system such that the error dynamics between master and slave chaotic systems is asymptotically stable. For verification of our theory, computer and circuit simulations f...

Following a recent suggestion by Nielsen, Rugh, and Rugh, we study the energy scaling of the maximal Lyapunov exponent of classical Hamiltonian SU(2) lattice gauge theory. It is shown that the conjectured scaling behavior λ0 ∼ E1/4 at small energies on the lattice is a finite-time artifact. New numerical results for the maximal Lyapunov exponent are presented for lattices up to size 20 and over...

In this paper we develop a theory of stabilizing singleinput nonlinear affine systems using quantized feedback. We construct a stabilizing quantizer based on a control Lyapunov function (CLF), and a robustly stabilizing quantizer based on a robust control Lyapunov function (RCLF). We characterize the coarsest quantizer under certain conditions. The special features of several classes of nonline...

The robust stabilization problem of chaos suppression for permanent magnet synchronous motors (PMSM) drive system is investigated in presence of parametric uncertainties. Based on control Lyapunov function (CLF) approach, a new state feedback controller is designed to realize the state of the system globally asymptotically stable. The stability of the proposed control scheme is verified via Lya...

Surveillance missions for multiple autonomous underwater vehicle (AUV) system suggest the use of different modes of operation including organizing and keeping a predefined formation, avoiding obstacles, reaching static and tracking dynamic targets. While exploiting a leader-follower strategy to formation control and the vector Lyapunov function method to controller design, we use discrete-event...

In this paper a convex optimization approach to design a robust state feedback control is proposed for DC-DC converter systems with mixed delays. Based on the Lyapunov theory, some required sufficient conditions are established in terms of delay-dependent linear matrix inequalities for the stochastic stability and stabilization of the considered system using some free matrices. The desired cont...