Abstract
Suppose that a collection of q real-valued variables, denoted by w, is observed in discrete time Z. The basic problem in system identification is to construct a system B that reflects the dynamic relations between these variables. Restricting the attention to linear systems, one of the principal choices are the number m of inputs and the number n of states of the system. For example, consider a stochastic input-output system y = Gu + Hε, where ε is a white noise process and G and H are rational transfer functions of sizes p × m and p × p respectively, with p + m = q. The system variables are w = (u, y), and m is equal to the number of unrestricted variables (the inputs u) and n is equal to the sum of the McMillan degrees of G and H.
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Heij, C. (1999). Selection of the number of inputs and states. In: Blondel, V., Sontag, E.D., Vidyasagar, M., Willems, J.C. (eds) Open Problems in Mathematical Systems and Control Theory. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-0807-8_24
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DOI: https://doi.org/10.1007/978-1-4471-0807-8_24
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