We show that there is a Lyapunov functional for the neural field equation, a neural network model which represents highly dense cortical neurons as a spatially continuous field, and that the system necessarily converges to an equilibrium point as far as the length of the field is finite. We also show that the Lyapunov functional is a natural extension of the Lyapunov function of the Hopfield mo...

The problem of pth mean exponential stability and stabilizability of a class of stochastic nonlinear and bilinear hybrid systems with unstable and stable subsystems is considered. Sufficient conditions for the pth mean exponential stability and stabilizability under a feedback control and stabilizing switching rules are derived. A method for the construction of stabilizing switching rules based...

Robot manipulators are now used in various domains and environments, where they can be subjected to random vibrations. Random vibrations mainly affect the torque control signal, a controller is therefore required designed for stabilization purposes. However, security or intellectual property protection reasons, most commercialized robots manufactured with unknown inaccessible interface such tha...

This paper presents a proof that the use of polynomial Lyapunov functions is not conservative for studying exponential stability properties of nonlinear ordinary differential equations on bounded regions. The main result implies that if there exists an n-times continuously differentiable Lyapunov function which proves exponential decay on a bounded subset of R, then there exists a polynomial Ly...

We consider an arbitrary number of interconnected nonlinear systems with time-delays and investigate them in view of input-to-state stability (ISS). The useful tools for single time-delay systems, the ISS Lyapunov-Razumikhin functions and ISS Lyapunov-Krasovskii functionals are redefined and applied to interconnected systems. By the help of a smallgain condition we prove that the whole system w...