ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

17. Control Theory and Optimization

1991 MS Classification: 46, 49 Perov, Anatolii, Voronezh State University, Russia Discrete matrix Lur’e equation (singular case). Positivity, monotonity and concavity of Lur’e operator. Analitic property of Lur’e operator. S. G. Semenov’s formula. Qualitative theory of Lur’e equation. The difference from orthogonal methods. Construction of the kernel of the stabilizing solution (when the solution is not known). Proof existence of stabilizing solution by the consecutive approachs method under the special choose of the cone. Therefore, the well known discrete frequency Kalman-Popov-Jacubovich theorem is proved by the consecutive approachs method. The work was supported by grant of Russian Basis Research Foundation (96-01-00374). Reference: A. I. Perov, Discrete matrix Lur’e equation (regular case), Automatics and Telemechanics, 3 (1995), 21-29.