A numerical method for computational implementation of gradient dynamical systems is presented. The method is based upon the development of geometric integration numerical methods, which aim at preserving the dynamical properties of the original ordinary differential equation under discretization. In particular, the proposed method belongs to the class of discrete gradients methods, which subst...

This paper studies the exponential stabilization problem for discrete-time switched linear systems based on a control-Lyapunov function approach. A number of versions of converse control-Lyapunov function theorems are proved and their connections to the switched LQR problem are derived. It is shown that the system is exponentially stabilizable if and only if there exists a finite integer N such...

where q : [a,b] → R is a continuous function, and the zeros a and b of every solution y(t) are consecutive. Since then, many generalizations of the Lyapunov inequality have appeared in the literature (see [–] and the references therein). Recently, the research of Lyapunov-type inequalities for fractional boundary value problem has begun. In [], Ferreira investigated a Lyapunov-type inequali...

We establish, as far as we know, the first proof of uniform global asymptotic stability for a mechanical system (Euler-Lagrange) in closed loop with a dynamic controller which makes use only of position measurements. The controller is fairly simple, it is reminiscent of the so-called PadenPanja controller [20] where unavailable generalized velocities are replaced by approximate differentiation ...

This paper includes results centered around three topics, all of them related with the nonlinear stability of equilibria in Poisson dynamical systems. Firstly, we prove an energy-Casimir type sufficient condition for stability that uses functions that are not necessarily conserved by the flow and that takes into account certain asymptotically stable behavior that may occur in the Poisson catego...

We investigate essential spectrum of the Euler equation linearized about an arbitrary smooth steady flow in dimension 3. It is proved that for every Lyapunov-Oseledets exponent μ of the associated bicharacteristic-amplitude system, the circle of radius e has a common point with the spectrum. If, in addition, μ is attained on an aperiodic point, then the spectrum contains the entire circle.

Stabilization involves finding feedback controllers which stabilize the closed-loop system in the finite-time sense. Stability and control have been developed in the literature using Lyapunov-like method. In this paper, we develop a general framework for stabilization of linear differential-algebraic equations with time-varying delay. Based on Lyapunov-like function method and new bound estimat...

The paper deals with connections between optimality and passivity-like properties in discrete time. The problem is set in the framework of differential/difference representations of discrete-time dynamics. The Hamilton–Jacobi–Bellman equality associated with a given cost and the corresponding optimal control solution are characterized. On these bases the connection with u-average passivity is c...

We investigate the planar quasi-septic non-analytic systems which have a center-focus equilibrium at the origin and whose angular speed is constant. The system could be changed into an analytic system by two transformations, with the help of computer algebra system MATHEMATICA, the conditions of uniform isochronous center are obtained. Keywords—Non-analytic; Center–focus problem; Lyapunov const...

where a, b Î R with a <b, and the constant 4 cannot be replaced by a larger number, where and in the sequel q(t) = max{q(t), 0}. Since then, there are many improvements and generalizations of (1.2) in some literatures. Especially, Lyapunov inequality has been generalized extensively to the higher-order linear equations and the linear Hamiltonian systems. A thorough literature review of continuo...