Minimal Realization Problems for Jump Linear Systems
Author(s)Sarkar, Tuhin; Roozbehani, Mardavij; Dahleh, Munther A
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This paper addresses two fundamental problems in the context of jump linear systems (JLS). The first problem is concerned with characterizing the minimal state space dimension solely from input-output pairs and without any knowledge of the number of mode switches. The second problem is concerned with characterizing the number of discrete modes of the JLS. For the first problem, we develop a linear system theory based approach and construct an appropriate Hankel-like matrix. The rank of this matrix gives us the state space dimension. For the second problem we show that minimal number of modes corresponds to the minimal rank of a positive semi-definite matrix obtained via a non-convex formulation.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
2018 IEEE Conference on Decision and Control (CDC)
Sarkar, T., et al. “Minimal Realization Problems for Jump Linear Systems.” 2018 IEEE Conference on Decision and Control (CDC), Miami Beach, Florida, USA, 17-19 December 2018, IEEE, 2018, pp. 5670–75.
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