Checkable conditions for identifiability of linear systems operating in closed loop

Necessary and sufficient conditions are given for the identifiability of the open-loop transfer functions for linear discrete time systems operating in closed loop. It is shown that, provided certain structural constraints are satisfied, it is necessary and sufficient that the noise covariance matrix Σ associated with any spectral factorization of the joint input-output spectral density be block diagonal. A continuity result is also established showing that small off-diagonal elements in the noise covariance lead to small errors in the estimated open-loop transfer functions. This extends previously known results which required that the true noise covariance be block diagonal.

[1]  G. Goodwin,et al.  Identifiability conditions for Continuous Time Linear Closed Loop Systems , 1979 .

[2]  J. M. Edmunds,et al.  Least-squares identification of closed-loop systems , 1975 .

[3]  B. Anderson.  The inverse problem of stationary covariance generation , 1969 .

[4]  Brian D. O. Anderson,et al.  Recursive algorithm for spectral factorization , 1974 .

[5]  L. Ljung,et al.  Identifiability conditions for linear systems operating in closed loop , 1975 .

[6]  Identifiability of Closed Loop Systems Using the Joint Input-Output Identification Method , 1979 .

[7]  G. Goodwin,et al.  On the Estimation of the Parameter of an Optimal Interpolator When the Class of Interpolators is Restricted , 1980 .

[8]  Peter E. Caines,et al.  Feedback between stationary stochastic processes , 1975 .

[9]  B. Anderson.  Algebraic properties of minimal degree spectral factors , 1973 .

[10]  C. W. J. Granger,et al.  Economic Processes Involving Feedback , 1963, Inf. Control..

[11]  S. Wu,et al.  Identification of multiinput-multioutput transfer function and noise model of a blast furnace from closed-loop data , 1974 .

[12]  Tung-Sang Ng,et al.  Identifiability of MIMO linear dynamic systems operating in closed loop , 1977, Autom..

[13]  Lennart Ljung,et al.  Identification of processes in closed loop - identifiability and accuracy aspects , 1977, Autom..

[14]  M. Denham,et al.  On the factorization of discrete-time rational spectral density matrices , 1975 .

[15]  D. Youla,et al.  On the factorization of rational matrices , 1961, IRE Trans. Inf. Theory.

[16]  L. Ljung,et al.  Identification of linear, multivariable systems operating under linear feedback control , 1974 .

[17]  K. Mrtensson.  On the matrix riccati equation , 1971 .

[18]  H. Akaike.  On the use of a linear model for the identification of feedback systems , 1968 .

[19]  J. Willems.  Least squares stationary optimal control and the algebraic Riccati equation , 1971 .

[20]  T. Bohlin.  On the problem of ambiguities in maximum likelihood identification , 1971 .