Minimal Realization Problems for Jump Linear Systems
Provides theoretical foundations for system identification of jump linear systems, addressing fundamental minimal realization problems for control theory practitioners.
This paper develops methods to determine the minimal state space dimension and number of discrete modes for jump linear systems from input-output data, using a Hankel-like matrix rank for state dimension and a non-convex rank minimization for mode count.
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.