11 research outputs found
Block Toeplitz determinants, constrained KP and Gelfand-Dickey hierarchies
We propose a method for computing any Gelfand-Dickey tau function living in
Segal-Wilson Grassmannian as the asymptotics of block Toeplitz determinant
associated to a certain class of symbols. Also truncated block Toeplitz
determinants associated to the same symbols are shown to be tau function for
rational reductions of KP. Connection with Riemann-Hilbert problems is
investigated both from the point of view of integrable systems and block
Toeplitz operator theory. Examples of applications to algebro-geometric
solutions are given.Comment: 35 pages. Typos corrected, some changes in the introductio
Lyapunov stability analysis of higher-order 2D systems
We prove a necessary and sufficient condition for the asymptotic stability of a 2D system described by a system of higher-order linear partial difference equations. We show that asymptotic stability is equivalent to the existence of a vector Lyapunov functional satisfying certain positivity conditions together with its divergence along the system trajectories. We use the behavioral framework and the calculus of quadratic difference forms based on four-variable polynomial algebra