Abstract
Large-scale dynamical interconnections of systems may not be well defined in the sense of having unique solutions for all inputs. We provide tests that show when the overall system is well defined. In a stochastic interconnected system, there is the additional problem that the composite system may be “stochastically ill defined” in the sense that derivatives of white noise may appear. We provide a test that shows when the interconnected systems is stochastically well defined. It is also demonstrated how to obtain a state-variable representation of the interconnected system, when one exists, on a subspace of the original descriptor-variable space.
All of our results are based on “structure algorithms” for singular systems which use stable numerical operations on the original system and interconnection matrices.
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This research was supported by NSF Grant ECS-8805932.
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Lewis, F.L., Beauchamp, G., Özçaldiran, K. et al. Large-scale dynamical interconnections of stochastic singular systems. Circuits Systems and Signal Process 10, 115–133 (1991). https://doi.org/10.1007/BF01183244
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DOI: https://doi.org/10.1007/BF01183244