Abstract
In this chapter we define a generalized notion of dissipativity that incorporates more information about a dynamical system than the standard form in Chap. 1. This is achieved by augmenting the system model with a linear system that serves as a virtual filter for the inputs and outputs. This dynamic extension is subsequently related to the frequency domain notion of integral quadratic constraints in Chap. 9. Here we derive stability and performance tests that extend those in earlier chapters to interconnections where the subsystems are dissipative with respect to the generalized definition. We present a similar generalization of the notion of equilibrium-independent dissipativity from Chap. 3, and extend the ADMM algorithm from Chap. 6 to search over supply rates that depend on filtered inputs and outputs.
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Meissen, C., Lessard, L., Arcak, M., Packard, A.K.: Compositional performance certification of interconnected systems using ADMM. Automatica 61, 55–63 (2015). http://dx.doi.org/10.1016/j.automatica.2015.07.027
Rufino Ferreira, A., Meissen, C., Arcak, M., Packard, A.: Symmetry Reduction for Performance Certification of Interconnected Systems (submitted)
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Arcak, M., Meissen, C., Packard, A. (2016). Dissipativity with Dynamic Supply Rates. In: Networks of Dissipative Systems. SpringerBriefs in Electrical and Computer Engineering(). Springer, Cham. https://doi.org/10.1007/978-3-319-29928-0_8
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DOI: https://doi.org/10.1007/978-3-319-29928-0_8
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