The asymptotic behavior for the Vlasov–Poisson–Fokker–Planck system in bounded domains is analyzed in this paper. Boundary conditions defined by a scattering kernel are considered. It is proven that the distribution of particles tends for large time to a Maxwellian determined by the solution of the Poisson–Boltzmann equation with Dirichlet boundary condition. In the proof of the main result, th...

The problem is posed to develop Lyapunov theory for diierential systems described by high-order diierential algebraic equations. The questions are how to verify positivity along solutions of functionals of the system variables, to compute their derivative along solutions, and conclude (asymptotic) stability from there.

In this paper, the C-conforming finite element method is analyzed for a class of nonlinear fourth-order hyperbolic partial differential equation. Some a priori bounds are derived using Lyapunov functional, and existence, uniqueness and regularity for the weak solutions are proved. Optimal error estimates are derived for both semidiscrete and fully discrete schemes. Keywords—Nonlinear fourth-ord...

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 ...

The discrete-time bounded-real lemma for nonminimal discrete systems is presented. Based on this lemma, rigorous necessary and sufficient conditions for the existence of positive definite solutions to the Lyapunov equation for n-dimensional (n-D) digital systems are proposed. These new conditions can be applied to n-D digital systems with n-D characteristic polynomials involving factor polynomi...

We present a scheme for the determination of control Lyapunov functions which can be used as a basis for numerical computations. Under the assumption of local asymptotic nullcontrollability we de ne the domain of asymptotic nullcontrollability. On this set a control Lyapunov function is de ned via an optimal control problem. It is then shown that this function can be characterized as the unique...

If a system is given by its transfer function then the stability of the system is determined hy the denominator polynomial and its corresponding Hurwitz matrix 7-{. Also the critical stability conditions are determined by its determinant det 7-{. The aim of this paper is to get a generalized Hurwitz matrix for polynomial matrices. In order to achieve that, we first obtain a relation between the...