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Unsolved Problems in Mathematical Systems and Control Theory by Vincent D. Blondel, Alexandre Megretski

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Problem 10.6

What is the characteristic polynomial of a

signal flow graph?

Andrew D. Lewis

Department of Mathematics & Statistics

Queen’s University

Kingston, ON K7L 3N6

Canada

andrew@mast.queensu.ca

1 PROBLEM STATEMENT

16445

2 DISCUSSION

Signal flow graphs for modelling system interconnections are due to Mason [3, 4]. Of course, when making such interconnections, the stability of the interconnection is nontrivially related to the open-loop transfer functions that weight the branches of the signal flow graph. There are at least two things to consider in the course of making an interconnection: (1) is the interconnection BIBO stable in the sense that ...

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