An equation of Lyapunov type

Lyapunov equation

This chapter is about numerical methods for a particular type of equation expressed as a matrix equality. The Lyapunov equation is the most common problem in the class of problems called matrix equations. Other examples of matrix equations: Sylvester equation, Stein equation, Riccati equation. Definition 5.0.1 Consider two square matrices A, W ∈ Rn×n. The problem to find a square matrix X ∈ Rn×...

On Lyapunov Control of the Duffing Equation

This brief addresses the robust asymptotic and BIB0(bounded-input bounded-output) stability of a class of linear shift-variant multidimensional systems. Using a shift-invariant comparisonsystem, necessary and sufficient conditions for the stability of the entirefamily of systems are derived.

Steklov – Lyapunov type systems ∗

In this paper we describe integrable generalizations of the classical Steklov– Lyapunov systems, which are defined on a certain product so(m) × so(m), as well as the structure of rank r coadjoint orbits in so(m) × so(m). We show that the restriction of these systems onto some subvarieties of the orbits written in new matrix variables admits a new r × r matrix Lax representation in a generalized...

Lyapunov Functionals for the Enskog Equation

Two Lyapunov functionals are presented for the Enskog equation. One is to describe interactions between particles with various velocities and another is to measure the L distance between two classical solutions. The former yields the time-asymptotic convergence of global classical solutions to the collision free motion while the latter is applied into the verification of the L stability of glob...

Estimates from the discrete-time Lyapunov equation