We consider the class of closed generic fluid networks (GFN) models. This class contains for example fluid networks under general work-conserving and priority disciplines. Within this abstract framework a Lyapunov method for stability of GFN models was proposed by Ye and Chen. They proved that stability of a GFN model is equivalent to the property that for every path of the model a Lyapunov lik...

IfK is a closed convex cone and if L is a linear operator having L (K) ⊆ K, then L is a positive operator on K and L preserves inequality with respect to K. The set of all positive operators on K is denoted by π (K). If K∗ is the dual of K, then its complementarity set is C (K) := {(x, s) ∈ K ×K | 〈x, s〉 = 0} . Such a set arises as optimality conditions in convex optimization, and a linear oper...

The practical stability of a nonlinear nonautonomous Caputo fractional differential equation is studied using Lyapunov like functions. The novelty of this paper is based on the new definition of the derivative of a Lyapunov like function along the given fractional differential equation. Comparison results using this definition for scalar fractional differential equations are presented. Several ...

We prove a converse Lyapunov theorem for almost sure stabilizability of controlled diffusions: given a stochastic system a.s. open loop stabilizable at the origin, we construct a lower semicontinuous positive definite function whose level sets form a local basis of viable neighborhoods of the equilibrium. This result provides, with the direct Lyapunov theorem proved in a companion paper, a comp...

This paper solves the problem of controlling linear continuous-time systems subject to control signals constrained in magnitude (maybe asymmetrically). A controller design methodology is proposed, based on using an asymmetric Lyapunov function, that avoids the discontinuities in the control vector components resulting from the application of a piecewise linear control law previously proposed. T...

The Lyapunov function plays an important role in the stability theory of dynamical systems. Its counterpart for discrete systems is not studied so much, though importance such increasing. In this letter, attempt made to construct a analog competitive Lotka-Volterra equation. For purpose, logarithmic defined and its effectiveness shown.

This paper focuses on the stability analysis of systems having a continuum of equilibria. Two notions that are of particular relevance to such systems are convergence and semistability. Convergence is the property whereby every solution converges to a limit point that may depend on the initial condition. Semistability is the additional requirement that all solutions converge to limit points tha...

In this paper, we present a method for computing a basin of attraction to a target region for polynomial ordinary differential equations. This basin of attraction is ensured by a Lyapunov-like polynomial function that we compute using an interval based branch-and-relax algorithm. This algorithm relaxes the necessary conditions on the coefficients of the Lyapunov-like function to a system of lin...