Abstract
Here x(t) and w(t) are N-component vectors describing the system and the external white noise; N is the dimension of the system with the N • N matrix A. In order to refine the analysis of the accuracy characteristics of synthesized systems in the presence of random disturbances, we need to investigate the statistical properties of the integral quadratic criterion. While the solution of the synthesis problem requires only information about the mean value of the functional, the choice of optimal dimension for finite-dimensional models, observers, and controllers, and of various alternatives by comparison of the random values of the integral quadratic criterion requires a complete statistical description of the functional, i.e., evaluation of the distribution density of the criterion. We propose a new approach to this problem, based on construction of the generating function of the sought criterion. Consider an integral criterion of the form
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