In this paper, we consider global asymptotic properties for an age-structured model of heroin use based on the principles of mathematical epidemiology where the incidence rate depends on the age of susceptible individuals. The basic reproduction number of the heroin spread is obtained. It completely determines the stability of equilibria. Using the direct Lyapunov method with Volterra type Lyap...

‎in this paper‎, ‎we study stability of fractional-order nonlinear dynamic systems by means of lyapunov‎ ‎method‎. ‎to examine the obtained results‎, ‎we employe the developed techniques on test examples‎.

Abslraet-Recent applications of absolute stability methods to robustness analysis have led to a rebirth of interest in this topic. This paper is concerned with the robust stability of feedback distributed parameter systems against nonlinear and random disturbances. Our analysis is based on the Lyapunov direct method. To derive a stochastic Lyapunov function, we introduce the special stochastic ...

A relaxation of Lyapunov’s direct method has been proposed recently that allows for an algorithmic construction of Lyapunov functions to prove stability of equilibria in nonlinear systems, but the search is restricted to systems with polynomial vector fields. In this paper, the above technique is extended to include systems with equality, inequality, and integral constraints. This allows certai...

In this paper, a direct adaptive control scheme for a class of nonlinear systems is proposed. The architecture employs a Gaussian radial basis function (RBF) network to construct an adaptive controller. The parameters of the adaptive controller are adapted and changed according to a law derived using Lyapunov stability theory. The centres of the RBF network are adapted on line using the kmeans ...

In this paper, we study the linear quadratic Nash games for infinite horizon singularly perturbed systems. In order to solve the problem, we must solve a pair of cross–coupled algebraic Riccati equations with a small positive parameter ε. As a matter of fact, we propose a new algorithm, which combines Lyapunov iterations and the generalized Lyapunov equation direct method, to solve the cross–co...

This paper addresses the visual servoing problem of a robot–pendulum in fixed–camera configuration. We present two new visual position controllers supported by a rigorous analysis of local asymptotic stability in agreement with the Lyapunov’s direct method and the LaSalle’s invariance principle. The proposed controllers belong to the family of Transpose Jacobian-based schemes. We also present t...

This paper deals with the problem of regional stability and performance analysis for a class of nonlinear discrete-time systems with uncertain parameters. We use polynomial Lyapunov functions to derive stability conditions and performance criteria in terms of linear matrix inequalities (LMIs). Although the use of polynomial Lyapunov functions is common for continuoustime systems as a way to red...