Lyapunov type equation for discrete exponential trichotomies

Exponential trichotomies and continuity of invariant manifolds

In this work, we consider the invariant manifolds for the family of equations ẋ = Ax + f(ε, x), where A the is generator of a strongly continuous semigroup of linear operators in a Banach space X and f(ε, ·) : X → X is continuous. The existence of stable (unstable) and center-stable (center-unstable) manifolds for a large class of these equations has been proved in [2]. We prove here that, if A...

Estimates from the discrete-time Lyapunov equation

Bounds for solutions of the discrete algebraic Lyapunov equation

A family of sharp, arbitrarily tight, upper and lower matrix bounds for solutions of the discrete algebraic Lyapunov are presented. The lower bounds are tighter than previously known ones. Unlike the majority of previously known upper bounds, those derived here have no restrictions on their applicability. Upper and lower bounds for individual eigenvalues and for the trace of the solution are fo...

Bounds for the solution of the discrete algebraic Lyapunov equation

New bounds for solutions of the discrete algebraic Lyapunov equation P = APA T + Q are derived. The new bounds are compared to existing ones and found to be of particular interest when A is non-normal.

Some Discrete Fractional Lyapunov–type Inequalities

In this work we obtain Lyapunov-type inequalities for two-point conjugate and rightfocal boundary value problems depending on discrete fractional operators Δα , 1 < α 2 .