We present a novel learning scheme to imprint stable vector fields into Extreme Learning Machines (ELMs). The networks represent movements, where asymptotic stability is incorporated through constraints derived from Lyapunov stability theory. We show that our approach successfully performs stable and smooth point-to-point movements learned from human handwriting movements.

In this paper, a system for P2P networks with discrete time delay based on game theory presented. This system is proposed to describe evolution procedure of the credibility of various members in the P2P network. Through analyzing the stability of the system model based on the Lyapunov stability theory, the conditions for Hopf bi furcation and stability are obtained. Finally, some numerical exam...

We study dynamical behavior of a class of cellular neural networks system with distributed delays under dynamical thresholds. By using topological degree theory and Lyapunov functions, some new criteria ensuring the existence, uniqueness, global asymptotic stability, and global exponential stability of equilibrium point are derived. In particular, our criteria generalize and improve some known ...

This paper addresses the stabilization issue for fractional order switching systems. Common Lyapunov method is generalized for fractional order systems and frequency domain stability equivalent to this method is proposed to prove the quadratic stability. Some examples are given to show the applicability and effectiveness of the proposed theory.

The notion of “strong stability” has been introduced in a recent paper [KHP2]. This notion is relevant for state-space models described by physical variables and prohibits overshooting trajectories in the state-space transient response for arbitrary initial conditions. Thus, “strong stability” is a stronger notion compared to alternative definitions (e.g. stability in the sense of Lyapunov or a...

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...

In this paper, the robust asymptotic stability for a class of uncertain neutral system with time delays are considered. Based on Lyapunov theory, some stability criteria are derived. Delay-dependent and delay-independent criteria are proposed for the stability of our considered systems. Linear matrix inequality (LMI) approach and genetic algorithms (GAS) are used to solve the stability problems...

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...

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...

In the stability theory of dynamical systems, Lyapunov functions play a fundamental role. In this paper, we study the attractor-repeller pair decomposition and Morse decomposition for compact metric space in the random setting. In contrast to [8], by introducing slightly stronger definitions of random attractor and repeller, we characterize attractor-repeller pair decompositions and Morse decom...