Passification with Respect to Given Input and Output for Linear SISO Systems
Автор(ы):
Alexander Lvovich Fradkov
Institute of Problems in Mechanical Engineering,
Russian Academy of Sciences, 199178, Saint Petersburg, Russia
Department of Theoretical Cybernetics,
Saint Petersburg State University, 199034, Saint Petersburg, Russia
Dr.Sc., Professor
fradkov@mail.ru
Mikhail Markovich Lipkovich
Institute of Problems in Mechanical Engineering,
Russian Academy of Sciences, 199178, Saint Petersburg, Russia
Department of Theoretical Cybernetics,
Saint Petersburg State University, 199034, Saint Petersburg, Russia
PhD in physics and mathematics
lipkovich.mikhail@gmail.com
Аннотация:
New version of passification with respect to given inputs and outputs is proposed.
It can be considered as an extension of passification
introduced in (Fradkov, IEEE CDC 2008).
Necessary and sufficient conditions for the proposed version of
passification are obtained for linear SISO systems.
Solution is based on KYP lemma and Meerov's results concerning
high gain stabilization.
Ключевые слова
- absolute stability
- KYP lemma
- linear systems
- Passification
Ссылки:
- Ajzerman, M. A. and Gantmacher, F. R. (1964). Absolute Stability of Regulator Systems. Holden-Day, San Francisco
- Arcak, M., Larsen, M. and Kokotovic, P. (2003). Circle and Popov criteria as tools for nonlinear feedback design. Automatica, vol. 39, no. 4, pp. 643-650
- Fradkov, A., Lipkovich, M. (2015). Adaptive absolute stability. IFAC-PapersOnLine, vol. 48, no. 11, pp. 258-263
- Fradkov, A., Lipkovich, M. (2016). Passification of MIMO linear systems with respect to given output. in Proc. of 2016 American Control Conference (ACC), pp. 7037 - 7041
- Fradkov, A. L. (1976). Quadratic Lyapunov functions in the adaptive stabilization problem of a linear dynamic plant. Siberian Math. J., no. 2, pp. 341-348
- Fradkov, A. L. (2003). Passification of nonsquare linear systems and feedback Yakubovich-Kalman-Popov Lemma. Europ. J. Contr., vol. 9, no. 6, pp. 573-582
- Fradkov, A. L. (2008). Passification of Linear Systems with Respect to Given Output. in Proc. of 47th IEEE CDC, pp. 646-651
- Jury, E. I. and Lee, B. W. (1964). On the absolute stability of a certain class of nonlinear sampled-data systems. IEEE Trans. Automatic Control, vol. 9, no. 1, pp. 51-61
- Kalman, R. E. (1963). Lyapunov functions for the problem of Lur'e in Automatic Control. Proc. Nation. Acad. Sci. USA, vol. 49, no. 2, pp. 201-205
- Lurie, A. I. (1951). Some nonlinear problems in the theory of automatic control. Gostekhizdat, Moscow. (in Russian)
- Lurie, A. I., Postnikov, V. N. (1944). On the theory of stability of control systems. Prikl. Matem. i Mekh., vol. 8, no. 3 (in Russian)
- Meerov, M. V. (1991). On the Routh-Hurwitz problem for equations containing small parameters. Automation and Remote Control. vol. 52, no. 7, pp. 934-940, 1991
- Popov, V. M. (1959). Criterii de stabilitate pentru sistemele neliniare de reglare automata bazate pe utilizarea transformatei laplace. Stud. Cerc. Energetica, vol. 9, no. 1, pp. 119-135
- Rozenvasser, E. N. (1963). The absolute stability of nonlinear systems. Autom. Remote Control, vol. 24, no. 3, pp. 283-291
- Tsypkin, Y. Z. (1964). Frequency criteria for absolute stability of nonlinear sampled-data systems. Autom. Remote Control, vol. 25, no. 3, pp. 261-267
- Yakubovich, V. A. (1962). The solution of certain matrix inequalities in automatic control theory. Soviet mathematics, vol. 3, no. 2, pp. 620-623
- Yakubovich, V. A., Leonov, G. A. and Gelig, A. Kh. (2004). Stability of Stationary Sets in Control Systems with Discontinuous Nonlinearities. World Scientific, Singapore