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Zbl 1104.93048
de la Sen, M.; Ibeas, A.
On the stability properties of linear dynamic time-varying unforced systems involving switches between parameterizations from topologic considerations via graph theory. (English)
[J] Discrete Appl. Math. 155, No. 1, 7-25 (2007). ISSN 0166-218X

Summary: This paper deals with the stability of linear time-varying systems involving switches through time between different parameterizations of a dynamic linear time-varying system. Graph theory is used to describe the combinations of possible switches of the various sets of parameterizations which ensure the stability of the configurations. Each graph vertex is associated with a particular parameterization while edges (arcs) are associated with switches between the graphs (directed graphs or digraphs). An axiomatic framework is first established concerned with previously known stability results from systems theory related to the achievement of stability when switches between several parameterizations of a dynamic system take place. The axiomatic context is then used to obtain stability results mainly based on the topology of the links between the various configurations associated with a state-trajectory as well as on the nature of the vertices related to the stability of the various isolated parameterizations.

MSC 2000:: *93D20 Asymptotic stability of control systems
93A05 Axiomatic system theory
93A30 Mathematical modelling of systems
90B10 Flows in networks
68R10 Graph theory in connection with computer science

Keywords: discrete mathematics; graph theory; stability; time-varying systems

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