Transformations for complex discrete linear Hamiltonian and symplectic systems

Symplectic Geometry and Hamiltonian Systems

1. Lecture

Complex fuzzy linear systems

Stability Radii of Linear Discrete{time Systems and Symplectic Pencils

In this paper, we introduce and analyze robustness measures for the stability of discrete-time systems x(t+1) = Ax(t) under parameter perturbations of the form A ! A + BDC where B; C are given matrices. In particular we characterize the stability radius of the uncertain system x(t+1) = (A+BDC)x(t), D an unknown complex perturbation matrix, via an associated symplectic pencil and present an algo...

Symplectic maps for approximating polynomial Hamiltonian systems.

We study how to approximate polynomial Hamiltonian systems by composition of symplectic maps. Recently, a number of methods preserving the symplectic character have appeared. However, they are not completely satisfactory because, in general, they are computationally expensive, very difficult to obtain or their accuracy is relatively low. The efficiency of a numerical method depends on both its ...

On Stability Zones for Discrete-time Periodic Linear Hamiltonian Systems

The main purpose of the paper is to give discrete-time counterpart for some strong (robust) stability results concerning periodic linear Hamiltonian systems. In the continuoustime version, these results go back to Liapunov and Žukovskii; their deep generalizations are due to Kreı̆n, Gel’fand, and Jakubovič and obtaining the discrete version is not an easy task since not all results migratemutati...