The State Space Extension Method in the Theory of Absolute Stability

IEEE Transactions on Automatic Control

Volumn 45, Issue 12, 2000, Pages 2335-2339

  Barabanov, Nikita E ^a  

^a SAINT PETERSBURG ELECTROTECHNICAL UNIVERSITY LETI   (Russian Federation)

Author keywords

Absolute stability; frequency domain criteria; nonlinear systems

Indexed keywords

ASYMPTOTIC STABILITY; FREQUENCY DOMAIN ANALYSIS; LYAPUNOV METHODS; MATHEMATICAL MODELS; STATE SPACE METHODS; UNCERTAIN SYSTEMS;

STATE SPACE EXTENSION METHODS;

SYSTEM STABILITY;

EID: 0034472063     PISSN: 00189286     EISSN: 15582523     Source Type: Journal    
DOI: 10.1109/9.895569     Document Type: Article

References (23)

1. R.W. Brockett and J. L.Willems, “Frequency domain stability criteria,” IEEE Trans. Automat. Contr., vol. AC-10, pp. 255-261, 401-413, 1965.
2. G. Zames, “On the input-output stability of nonlinear time-varying feedback systems-Part I: Conditions derived using concepts of loop gain, and Part II: Conditions involving circles in the frequency plane and sector nonlinearities,” IEEE Trans. Automat. Contr., vol. 11, pp. 228-238, Apr. 1966.
3. G. Zames and P. L. Falb, “Stability conditions for systems with monotone and slope-restricted nonlinearities,” SIAM J. Contr., vol. 6, no. 1, pp. 89-108, 1968.
4. V. M. Popov, “Absolute stability of nonlinear systems of automatic control,” Automat. Remote Contr., vol. 22, pp. 857-875, Mar. 1962. Russian original in Aug. 1961.
5. V. A. Yakubovich, “The method of matrix inequalities in the theory of stability of nonlinear control systems-Parts I-III,” Avtomatica i Telemechanica, vol. 25, no. 7, pp. 1017-1029, 1964. (English translation in Automat. Remote Contr.).
6. “Frequency domain theorem in the control theory,” Siberian Math. J., no. 2, pp. 384-420, 1973.
7. A. Megretski and A. Rantzer, “System analysis via integral quadratic constraints,” IEEE Trans. Automat. Contr., vol. 42, pp. 819-830, 1997.
8. N. E. Barabanov, “State space extension method in the theory of stability of automatic control systems,” Ph.D. dissertation, Inst. Cybernetics, Kiev, USSR, 1990.
9. “Frequency domain and instability stability criteria of differential equations with a single monotone nonlinearity,” Siberian Math. J., no. 2, pp. 5-14, 1987.
10. “New frequency domain stability and instability criteria of automatic control systems with time-varying nonlinearities” (in Russian), Differential Equations, vol. 25, no. 4, pp. 555-563, 1989.
11. “Criteria for global asymptotics of stationary sets of systems containing a hysteresis nonlinearity” (in Russian), Differential Equations, vol. 25, no. 5, pp. 739-748, 1989.
12. V. A. Yakubovich, S-procedure in nonlinear control theory, Vestnik Leningrad Univ., pp. 62-77, 1977.
13. “Absolute stability of nonlinear control systems, Part I: General frequency domain criteria,” Avtomatica i Telemechanica, no. 12, pp. 5-14, 1970. (English translation in Automat. Remote Contr.).
14. A. H. Gelig, G. A. Leonov, and V. A. Yakubovich, Stability of Nonlinear Systems with Nonunique Equilibrium State (in Russian). Leningrad: Nauka, 1978.
15. N. E. Barabanov, “On the possibility of improving of frequency domain stability criteria” (in Russian), Syst. Dynamics, vol. 6, pp. 61-68.
16. K. S. Narendra and J. H. Taylor, Frequency Domain Criteria for Absolute Stability. New York: Academic, 1973.
17. Y. Venkatesh, Energy Methods in Time-Varying Stability and Instability Analysis. Berlin, Germany: Springer-Verlag, 1977.
18. C. A. Desoer and M. Vidyasagar, Feedback Systems: Input-Output Properties. New York: Academic, 1975.
19. N. E. Barabanov, “On the Kalman conjecture” (in Russian), Siberian Math. J., vol. 3, pp. 5-12, 1988.
20. A. L. Lihtarnikov and V. A. Yakubovich, “Abstract control theory” (in Russian), in Absolute Stability of Automatic Control Systems with Delay, V. Rezvan, Ed. Moscow: Nauka, 1983.
21. V. A. Yakubovich, “The method of matrix inequalities in the theory of stability of nonlinear control systems-Parts I-III,” Avtomatica i Telemechanica, vol. 26, no. 4, pp. 577-599, 1964. (English translation in Automat. Remote Contr.).
22. V. A. Yakubovich, “The method of matrix inequalities in the theory of stability of nonlinear control systems-Parts I-III,” Avtomatica i Telemechanica, vol. 26, no. 5, pp. 753-763, 1964. (English translation in Automat. Remote Contr.).
23. V. A. Yakubovich, S-procedure in nonlinear control theory (in English), Vestnik Leningrad Univ. Math., vol. 4, pp. 73-93, 1977.