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Русская версия

**I. E. Zuber**

Russia, 198904, Saint-Petersburg,

Petrodvoretz, Bibliotechnaya pl., 2,

Saint-Petersburg State University,

Department of mathematics and mechanics,

Consider matrix-vector form of nonlinear time-varying discrete system and its similarity transformations. We shall consider a similarity transformation as a canonical transformation if object's matrix of transformed system is the Frobenious matrix. We shall consider a similarity transformation as a canonical transformation if the matrix of closed loop transformed system is the Frobenious matrix. Sufficient conditions of existence and explicit form of canonical transformation are obtained. Theorem 1. If sufficient conditions of canonical transformation's existence are fulfilled then exists an can be obtained in explicit form the feed-back vector which provides the global stability of closed loop system. Theorem 2. If the conditions of existence of canonical transformation are fulfilled then exists and can be obtained in explicit form the feed-back vector for which the closed loop system is similar to linear time-stationary system.