We study the dynamics of perturbations in time-delay dynamical systems. Using a suitable space-time coordinate transformation, we find that the time evolution of the linearized perturbations (Lyapunov vector) can be described by the linear Zhang surface growth model [J. Phys. (France) 51, 2129 (1990)]], which is known to describe surface roughening driven by power-law distributed noise. As a co...

Epilepsy is a very common neurological disorder. Electroencephalogram (EEG) is the major diagnostic tool used for analyzing the human epileptic seizure activity and there is a strong need of an efficient automatic seizure detection using it to ease the diagnosis. This work aims at an automatic system for diagnosis of epilepsy. Here we extract some features like fractal dimensions, sample entrop...

A piecewise quadratic Lyapunov function is developed for the analysis of the global and regional performances for systems with saturation/deadzone in a general feedback configuration with an algebraic loop. This piecewise quadratic Lyapunov function effectively incorporates the structure of the saturation/deadzone nonlinearity. Several sector-like conditions are derived to describe the complex ...

This paper investigates the problem of global consensus between a complex dynamical network (CDN) and a known goal signal by designing an impulsive consensus control scheme. The dynamical network is complex with respect to the uncertainties, nonidentical nodes, and coupling time-delays. The goal signal can be a measurable vector function or a solution of a dynamical system. By utilizing the Lya...

This paper presents an investigation into the design of a flight control system, using a robust backstepping control structure, designed using the two-time scale control procedure of the dynamic of a small-size autonomous helicopter in hover. The two-time scale controller takes advantage of the ‘decoupling’ of the translational and rotational dynamics of the rigid body, resulting in a two-level...

We analyze stability for switched systems which are composed of both continuous-time and discrete-time subsystems. By considering a Lie algebra generated by all subsystem matrices, we show that if all subsystems are Hurwitz/Schur stable and this Lie algebra is solvable, then there is a common quadratic Lyapunov function for all subsystems and thus the switched system is exponentially stable und...

Asymptotic linear stability of time-dependent flows is examined by extending to nonautonomous systems methods of nonnormal analysis that were recently developed for studying the stability of autonomous systems. In the case of either an autonomous or a nonautonomous operator, singular value decomposition (SVD) analysis of the propagator leads to identification of a complete set of optimal pertur...

The paper considers a class of additive neural networks where the neuron activations are modeled by discontinuous functions or by continuous non-Lipschitz functions. Some tools are developed which enable us to apply a Lyapunov-like approach to differential equations with discontinuous right-hand side modeling the neural network dynamics. The tools include a chain rule for computing the time der...