Investigation and Simulating of Algorithm of Building of Set of Attainability of Linear Controlled System

Sets of attainability in phase state space represent one of the main characteristics of controlled systems. The basic investigation concerned with building of foregoing sets for discrete and continuous systems is executed according to the set- theoretical (guaranteed) approach of tasks with uncertainty (Chernous´ko, 1996; Kurzhanskii, 1982). Ellipsoidal approximations of required sets on the basis of the ellipsoid method of this approach - the most effective approach of the constructive solution of guaranteed estimation tasks. The brief review of the most important investigations in the field of guaranteed estimation of sets of attainability is possible to find in introduction to article (Chernous´ko, 2002). For discrete-continuous linear system with one input more simple as compared to general case 121 algorithm of building of sets of attainability is proposed. The offered variant of algorithm is not required of simultaneous reduction of quadratic forms to canonical form. In the basis of new solution is using of stretching (compressing) operator (Shor, 1983).