Identifiability of a multivariable closed-loop stochastic system. Decomposition of a closed-loop system in identification

Two aspects of the problem of identifying a multivariable stochastic system are discussed: identifiability of a closed-loop system and the possibility of decomposing a system in identification. Truncated likelihood functions are introduced. Certain elements of the plant and certain closed loops can be identified without concurrent identification of the other elements and loops of the system. Sufficient conditions of convergence almost certainly of the estimates of truncated likelihood to the true values with increase of the sample size. The necessary and sufficient conditions of structural nonidentifiability are obtained in a closed-loop multivariable circuit, or conditions under which the plant cannot be identified under any values of the system parameters. Ways to eliminate structural nonindentifiability are proposed.