Professor Vladimir A. Yakubovich

Head of Theoretical Cybernetics Branch

V.A. Yakubovich is one of the creators of the modern Control Theory. His result on the solution of certain special matrix inequalities, published in Doklady AN SSSR in 1962, is widely known now. Improved by R. Kalman in 1963 and then by V.M. Popov, this result is called now the KY-lemma or the KYP-lemma. The KY-lemma was applied and is still being applied in a lot of papers, devoted to problems in diverse areas such as adaptation, stability, optimal control and strange attractors.

The results by V.A. Yakubovich in absolute stability theory have also become very well known. They concern systems, which now are called uncertain. After V.M. Popov has obtained his striking "frequency domain stability criterion", it seemed that the Liapunov function method exhausted itself and that it is less powerful that the frequency method, suggested by Popov. By applying the KY-lemma Yakubovich found out a new proof of the Popov criterion, based on the Liapunov function method and also obtained new absolute stability criteria, which restored the confidence in this method. Moreover, since various properties of a control system can be expressed in terms of Liapunov functions and the KY-lemma yields "frequency" conditions for the existence of a Liapunov function that can be verified effectively, a new "frequency" method for studying nonlinear systems appeared.

Following these ideas, V.A. Yakubovich and his students obtained diverse results concerning the qualitative study of nonlinear control systems. Many researches have used repeatedly the KY-lemma to establish the frequency estimates of the dimension of strange attractors.

A large cycle of papers by V.A. Yakubovich is devoted to the optimal control. In a series of papers in the Siberian Mathematical Journal he constructed an original theory of optimal control, which embraces as a particular case the theory by Pontryagin and his well-known colleagues. The advantages of this theory are that the proofs are simpler and that it can be applied to many new situations.

The linear-quadratic optimization problems, which are of practical importance, were studied thoroughly ( Siberian Math. J. 27, no. 4 (1986), 181--200; 31, no. 6 (1990), 176--191; Engl. translations exist). The KY-lemma was extended to the case of systems with periodic coefficients. In the work in Systems & Control Letters 19 (1992), 13--22 and in other papers, the case of quadratic constraints was studied. A method of global optimization was suggested, which can be applied to both convex and nonconvex problems. The latter application is surprising and important.

Yakubovich seems to be one of the first who began to develop the Adaptive Systems Theory ( Doklady AN SSSR 166, no. 6 (1966), 1308--1318; 183, no. 2 (1968), 303--306 and others; for a detailed exposition see the collection Voprosy Kibernetiki, Adaptivnye sistemy; Moscow, AN SSSR, 1974). In these works, the so-called recursive inequalities method was developed; it has been employed in the construction of adaptive regulators in many papers by Russian authors, but seems to be scarcely known in the West.

Vladimir Yakubovich is a member of a number of Scientific-Technical Councils on Automatization and Instrument-making. He is a corresponding member of Russian Academy of Sciences and the member of the Academy of Natural Sci. of Russia. He is the recipient of the Norbert Wiener Award for the contribution to Cybernetics (1992) and the recipient of IEEE Control Systems Award with the following citation: "For pioneering and fundamental contribution to stability analysis and optimal control".

Vladimir Yakubovich has created and educated a large scientific group; more than 30 of his pupils have obtained their Ph.D. degrees and 6 also their (second) Doctor degree. A lot of his firmer students live now and successfully work in USA, Japan, Australia, Sweden and other countries.