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Input-output parametric models for nonlinear systems. II: Stochastic nonlinear systems. (English) Zbl 0569.93012
This is a continuation of the material in part I [see the article reviewed above], which gives the basic result of existence of i/o equations under a nondegeneracy assumption on the linear part of the given response (or state space representation). Part 2 is devoted to examples and in particular to a comparison with the global (but implicit, rather than recursive) representations in the reviewer’s work. For some special models (”Wiener” and ”Hammerstein” models of cascades of linear systems and memory free nonlinearities), more explicit constructions are given. Finally, some discussion is included about stochastic versions of the results given in part I.
Reviewer: E.Sontag

MSC:
93B15 Realizations from input-output data
93C10 Nonlinear systems in control theory
93C55 Discrete-time control/observation systems
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
93E03 Stochastic systems in control theory (general)
93C35 Multivariable systems, multidimensional control systems
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[1] Billings S. A., PROC. INSTN ELECT. ENGRS 127 pp 272– (1980)
[2] Billings S. A., PROC. 7TH I.F.A.C. SYMP. ON IDENTIFICATION AND SYSTEM PARAMETER ESTIMATION (1985)
[3] Billings S. A., AUTOMATICA 18 pp 15– (1982) · Zbl 0472.93067
[4] Billings , S. A. , AND Leontaritis , I. J. , 1981 ,PROC. I.E.E. CONF. ON CONTROL AND ITS APPLICATIONS, Warwick , p. 183 ; 1982, Proc. 6th I.F.A.C. Symp. on Identification and System Parameter Estimation, Washington, D.C., p. 427.
[5] BILLINGS S. A., Proc. Inst, elect. Engrs 130 pp 193– (1983)
[6] CROUCH P. E., SI AM J. Control Optim. 19 pp 177– (1981) · Zbl 0477.93016
[7] GOODWIN G. C., Dynamic System Identification Experiment Design and Data Analysis (1977) · Zbl 0578.93060
[8] LEONTARITIS I. J., Int. J. Control 41 pp 303– (1984) · Zbl 0569.93011
[9] PADULO L., System Theory; A State-Space Approach to Continuous and Discrete-Time Systems (1974) · Zbl 0317.93001
[10] PAPOULIS A., Probability, Random Variables and Stochastic Processes (1965) · Zbl 0191.46704
[11] SONTAG , E. D. , 1976 , Ph.D. dissertation , University of Florida ; 1979a, Polynomial Response Maps, Lecture notes in Control and Information Sciences 13 (Berlin Springer-Verlag);1979b, I.E.E.E. Trans. Circuits Syst., 26, 342 .
[12] WERTZ V., I.E.E.E. Trans, autom. Control 27 pp 1200– (1982) · Zbl 0503.93066
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