×

Realization of truncated impulse response sequences with prescribed uncertainty. (English) Zbl 0535.93011

Control science and technology for the progress of society, Proc. 8th trienn. World Congr. IFAC, Kyoto 1981, Vol. 1, Control theory, 7-12 (1982).
Summary: [For the entire collection see Zbl 0518.00012.]
Many algebraic algorithms have been described in the literature to compute a discrete time state space realization of a system with a known impulse response. Six years ago L. S. de Jong [Diss. Technische Hogeschool Eindhoven (1975; Zbl 0305.93015)] focused attention on the numerical stability of these algorithms when using finite precision arithmetic. Only recently however, full attention has been paid to the problem of measurement noise, where the uncertainty level on the available data is fixed by the measurement configuration. Accepting this as a fact of life we consider the problem of finding an approximate state space model that takes into account all modes of the signal which are distinguishable from the noise i.e. all modes which have a signal-to- noise-ratio better than a required minimum. General properties and an algorithm for the solution of this problem are given. We obtain conclusions on the extractability of modes and useful schemes for the automatic setting of decision parameters necessary for practical implementation. From a practical point of view, the numerical qualities and the behaviour of the particular class of one-time-step-matching algorithm on noisy data are shown in a feasability study.

MSC:

93B20 Minimal systems representations
93C35 Multivariable systems, multidimensional control systems
93E25 Computational methods in stochastic control (MSC2010)
62J10 Analysis of variance and covariance (ANOVA)
70G10 Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics
93C05 Linear systems in control theory

Software:

EISPACK