7,326 research outputs found
Block-Diagonal Solutions to Lyapunov Inequalities and Generalisations of Diagonal Dominance
Diagonally dominant matrices have many applications in systems and control
theory. Linear dynamical systems with scaled diagonally dominant drift
matrices, which include stable positive systems, allow for scalable stability
analysis. For example, it is known that Lyapunov inequalities for this class of
systems admit diagonal solutions. In this paper, we present an extension of
scaled diagonally dominance to block partitioned matrices. We show that our
definition describes matrices admitting block-diagonal solutions to Lyapunov
inequalities and that these solutions can be computed using linear algebraic
tools. We also show how in some cases the Lyapunov inequalities can be
decoupled into a set of lower dimensional linear matrix inequalities, thus
leading to improved scalability. We conclude by illustrating some advantages
and limitations of our results with numerical examples.Comment: 6 pages, to appear in Proceedings of the Conference on Decision and
Control 201
Diagonal Riccati Stability and Applications
We consider the question of diagonal Riccati stability for a pair of real
matrices A, B. A necessary and sufficient condition for diagonal Riccati
stability is derived and applications of this to two distinct cases are
presented. We also describe some motivations for this question arising in the
theory of generalised Lotka-Volterra systems
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