Discrete linear Hamiltonian systems: Lyapunov type inequalities, stability and disconjugacy criteria

Lyapunov inequalities and stability for linear Hamiltonian systems

Linear Hamiltonian Difference Systems: Disconjugacy and Jacobi-Type Conditions

We consider a linear Hamiltonian Difference System for the so-called singular case so that discrete Sturm]Liouville Equations of higher order are included in our theory. We introduce the concepts of focal points for matrix-valued and generalized zeros for vector-valued solutions of the system and define disconjugacy for linear Hamiltonian Difference Systems. We prove a Reid Roundabout Theorem w...

Lyapunov-type inequalities and disconjugacy for some nonlinear difference system

*Correspondence: [email protected] 1College of Science, Hunan University of Technology, Zhuzhou, Hunan 412007, P.R. China Full list of author information is available at the end of the article Abstract We establish several new Lyapunov-type inequalities for some nonlinear difference system when the end-points are not necessarily usual zeros, but rather generalized zeros. Our results general...

Lyapunov-type inequalities for the first-order nonlinear Hamiltonian systems

In this paper, we establish several new Lyapunov-type inequalities for the first-order nonlinear Hamiltonian system  x ′ (t) = α(t)x(t) + β(t)|y(t)| µ−2 y(t), y ′ (t) = −γ (t)|x(t)| ν−2 x(t) − α(t)y(t), which generalize or improve all related existing ones.

Stability Criteria via Common Non-strict Lyapunov Matrix for Discrete-time Linear Switched Systems

Let S = {S 1, S 2} ⊂ Rd×d have a common, but not necessarily strict, Lyapunov matrix (i.e. there exists a symmetric positive-definite matrix P such that P − S T k PS k ≥ 0 for k = 1, 2). Based on a splitting theorem of the state space Rd (Dai, Huang and Xiao, arXiv:1107.0132v1[math.PR]), we establish several stability criteria for the discrete-time linear switched dynamics xn = S σn · · · S σ1 ...