Computational Psychiatry by Rodrick Wallace

Author:Rodrick Wallace
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(5.4)

where x t is the n-dimensional state vector at time t, u t is the imposed n-dimensional control signal vector at time t, W t is an added noise signal, and A and B are, in this approximation, n × n fixed matrices. See Fig. 5.2 for a schematic. Then the necessary condition for stabilizability is

(5.5)

where det is the determinant and A u is the decoupled unstable component of A, i.e., the part having eigenvalues ≥ 1. The determinant represents a generalized volume. Thus there is a critical positive data rate below which there does not exist any quantization and control scheme able to stabilize an unstable system (Nair et al. 2007).

Fig. 5.2“Regression model” for a control system near a nonequilibrium steady state. x t is system output at time t, u t the control signal, and W t an added noise term

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