Guaranteed value of the quadratic criterion for quality of linear system operation (Q1920374)

The main objective of the paper is to estimate a bound for a covariance matrix of a final state of a system disturbed by a scalar random process with zero expectation and limited variance. The problem is formulated in terms of maximization for a quadratic criterion of the final state over the set of admissible random processes, and both the maximal value of the index and the form of the maximizing process is determined. The author finds the optimal solution by simply selecting the vertices of the hypercube resulting from the bounds on the disturbing process. Although the procedure is completed in a finite number of steps this number might be prohibitively high. The main results are presented in two theorems giving necessary and sufficient conditions for the maximization and constitute a component part of the minimax control design. The optimization procedure is illustrated by a simple example in which the solution is obtained after 20 iterations.