The frequency theorem for equations of evolutionary type
Article
Received:
- 21 Downloads
- 10 Citations
Keywords
Evolutionary Type Frequency Theorem
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
Literature Cited
- 1.V. A. Yakubovich, “Solution of certain matrix inequalities encountered in automatic regulation theory,” Dokl. Akad. Nauk SSSR,143, No. 6, 1304–1307 (1962).Google Scholar
- 2.R. E. Kalman, “Lyapunov functions for the problem of Lur'e in automatic control,” Proc. Nat. Sci. USA,49, 201–205 (1963).Google Scholar
- 3.V. M. Popov, Hyperstability of Automatic Systems [in Russian], Nauka, Moscow (1970), pp. 94–97, 319–361.Google Scholar
- 4.V. A. Yakubovich, “The frequency theorem in control theory,” Sibirsk. Matem. Zh.,14, No. 2, 384–419 (1973).Google Scholar
- 5.M. A. Aizerman and F. P. Gantmakher, Absolute Stability of Regulatable Systems [in Russian], Izd. Akad. Nauk SSSR, Leningrad (1963), pp. 1–60.Google Scholar
- 6.F. R. Gantmakher and V. A. Yakubovich, “Absolute stability of nonlinear regulatable systems,” in: Proceedings of the 2nd All-Union Congress on Theoretical and Practical Mechanics [in Russian], Nauka, Moscow (1965), pp. 30–63.Google Scholar
- 7.D. Siljak, Nonlinear Systems, Wiley, New York-London-Sydney-Toronto (1969).Google Scholar
- 8.E. B. Lee and L. Markus, Foundations of Optimal Control Theory, Wiley, New York-London-Sydney-Toronto (1967).Google Scholar
- 9.V. A. Yakubovich, in: Investigation Methods for Nonlinear Automatic Control Systems [in Russian], R. P. Nelepin (editor), Nauka, Moscow (1975), Chaps. 2–3, pp. 74–180.Google Scholar
- 10.E. A. Noldus, “Frequency domain approach to the problem of existence of periodic motion in autonomous nonlinear feedback systems,” Z. Angew. Math. und Mech.,49, No. 3, 167–175 (1969).Google Scholar
- 11.V. A. Yakubovich, “Frequency conditions for self-oscillations in nonlinear systems with one stationary nonlinearity,” Sibirsk. Matem. Zh.,14, No. 5, 1100–1129 (1973).Google Scholar
- 12.G. A. Leonov, “Frequency conditions for the existence of nontrivial periodic solutions in autonomous systems,” Sibirsk. Matem. Zh.,14, No. 6, 1259–1265 (1973).Google Scholar
- 13.G. A. Leonov, “On one class of nonlinear differential equations for which the question of the existence of bounded and periodic solutions can be solved effectively,” Vestnik Leningr. Univ., Ser. Matem., Mekhan., Astron., No. 19, Issue 4, 29–32 (1972).Google Scholar
- 14.A. A. Fradkov, “Synthesis of an adaptive system for the stabilization of a dynamic plant,” Avtomat. i Telemekhan., No. 12, 96–103 (1974).Google Scholar
- 15.A. A. Fradkov, “Quadratic Lyapunov functions in the adaptive stabilization problem for a linear dynamic plant,” Sibirsk. Matem. Zh.,17, No. 2, 436–445 (1976).Google Scholar
- 16.V. A. Andreev, Yu. F. Kazarinov, and V. A. Yakubovich, “Synthesis of optimal controls for homogeneous linear systems in the minimization problems for quadratic functionals,” Dokl. Akad. Nauk SSSR,199, No. 2, 257–261 (1971).Google Scholar
- 17.V. A. Andreev and D. A. Plyako, “On one optimal control problem for an inhomogeneous linear system,” Sibirsk. Matem. Zh.,14, No. 3, 660–665 (1973).Google Scholar
- 18.V. A. Andreev, “Synthesis of optimal controls for inhomogeneous linear systems with a quadratic performance index,” Sibirsk. Matem. Zh.,13, No. 3, 698–702 (1972).Google Scholar
- 19.P. Faurre, “Identification par minimisation d'une représentation markovienne de processus aléaire,” in: Lecture Notes in Mathematics, Vol. 132, Springer-Verlag, Berlin-Heidelberg-New York (1970). pp. 85–106.Google Scholar
- 20.P. Faurre and I. P. Marmorat, “Une algorithme de realisation stochastique,” Compt. Rend. Acad. Sci. Paris,268, Ser. A, 978–981 (1969).Google Scholar
- 21.P. Faurre, “Identification of markovian representation of stochastic processes,” in: 4th Hawaii Internat. Conf. System Sciences, Jan. 12–14, 1971, Honolulu (1971), pp. 576–578.Google Scholar
- 22.J. L. Lions, Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag (1971).Google Scholar
- 23.V. A. Yakubovich, “The frequency theorem for the case when the state and control spaces are Hilbertian and its application to certain optimal control synthesis problems. II,” Sibirsk. Matem. Zh.,16, No. 5. 1081–1102 (1975).Google Scholar
- 24.Yu. M. Berezanskii, Eigenfunction Expansion of Self-Adjoint Operators [in Russian], Naukova Dumka, Kiev (1965), pp. 45–82.Google Scholar
- 25.J. L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, Springer-Verlag (1972).Google Scholar
- 26.S. G. Krein, Linear Differential Equations in Banach Space [in Russian], Nauka, Moscow (1967), pp. 58–75, 182–185.Google Scholar
- 27.V. A. Brusin, “On the existence of global Lyapunov functions for nonlinear distributed systems,” in: Dynamic Systems [in Russian], No. 7, Izd. Gor'k. Un-ta, Gor'kii (1975), pp. 18–34.Google Scholar
- 28.V. A. Yakubovich, “The frequency theorem for the case when the state and control spaces are Hilbertian and its application to certain optimal control synthesis problems. I,” Sibirsk. Matem. Zh.,15, No. 3, 639–668 (1974).Google Scholar
Copyright information
© Plenum Publishing Corporation 1977