Abstract
This chapter introduces a class of interconnected systems and derives a stability test from the dissipativity characteristics of the subsystems. This test has the form of a linear matrix inequality (LMI) which means that it can be checked with standard convex optimization packages. The decision variables of this LMI serve as the coefficients of a Lyapunov function constructed from the storage functions associated with the dissipativity properties of the subsystems. The rest of the chapter specializes this stability test to subsystems with first finite \(L_2\) gain and, next, passivity properties. Further elaborating on passivity, the last section identifies special interconnection structures where the feasibility of the LMI has analytical characterizations that give insight into the interplay between interconnection structure and stability properties.
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Notes
- 1.
Simple cycles are cycles with no repeated vertices other than the starting and ending vertexes.
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Arcak, M., Meissen, C., Packard, A. (2016). Stability of Interconnected Systems. In: Networks of Dissipative Systems. SpringerBriefs in Electrical and Computer Engineering(). Springer, Cham. https://doi.org/10.1007/978-3-319-29928-0_2
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DOI: https://doi.org/10.1007/978-3-319-29928-0_2
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