2017/09/20 by Aivar Sootla, Yang Zheng, Sootla, Aivar +3 · 3 citations
Engineering · Biochemistry, Genetics and Molecular Biology · #Stability and Control of Uncertain Systems #Control and Stability of Dynamical Systems #Gene Regulatory Network Analysis
paper · pdf · doi:10.48550/arxiv.1709.06809
Diagonally dominant matrices have many applications in systems and control\ntheory. Linear dynamical systems with scaled diagonally dominant drift\nmatrices, which include stable positive systems, allow for scalable stability\nanalysis. For example, it is known that Lyapunov inequalities for this class of\nsystems admit diagonal solutions. In this paper, we present an extension of\nscaled diagonally dominance to block partitioned matrices. We show that our\ndefinition describes matrices admitting block-diagonal solutions to Lyapunov\ninequalities and that these solutions can be computed using linear algebraic\ntools. We also show how in some cases the Lyapunov inequalities can be\ndecoupled into a set of lower dimensional linear matrix inequalities, thus\nleading to improved scalability. We conclude by illustrating some advantages\nand limitations of our results with numerical examples.\n