Absolute stability criteria with prescribed decay rate for finite-dimensional and delay systems

Automatica

Volumn 38, Issue 11, 2002, Pages 2015-2019

  Bliman, Pierre Alexandre ^a  

^a INRIA   (France)

Author keywords

stability; Absolute stability; Delay analysis; Frequency domains; Linear matrix inequality; Lyapunov function; Popov criterion

Indexed keywords

ALGORITHMS; FREQUENCY DOMAIN ANALYSIS; LYAPUNOV METHODS; MATRIX ALGEBRA; NONLINEAR CONTROL SYSTEMS; SYSTEM STABILITY;

DECAY RATES;

DELAY CONTROL SYSTEMS;

EID: 0036836976     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0005-1098(02)00092-4     Document Type: Article

References (15)

1. Aizerman M.A., Gantmacher F.A. Absolute stability of regulator systems. 1964;Holden-Day, San Francisco, CA.
2. Bliman, P.-A. (1999). Extension of Popov criterion to time-varying nonlinearities: LMI, frequential and graphical conditions. In Aeyels, D., Lamnabhi-Lagarrigue, F., van der Schaft, A. (Eds.), Stability and stabilization of nonlinear systems, Lecture notes in control and information sciences, vol. 246 (pp. 95-114). Berlin, Heidelberg: Springer.
3. Bliman P.-A. Extension of Popov absolute stability criterion to nonautonomous systems with delays. International Journal of Control. 73(15):2000;1349-1361.
4. Bourlès H. α -stability and robustness of large-scale interconnected systems International Journal of Control. 36:1987;2221-2232.
5. Boyd, S., El Ghaoui, L., Feron, E., & Balakrishnan, V. (1994). Linear matrix inequalities in system and control theory. SIAM Studies in Applied Mathematics, 15. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, USA.
6. Corduneanu, C. (1972). Absolute stability of some integro-differential systems. Ordinary differential equations (Proc. Conf., Math. Res. Center, Naval Res. Lab., Washington, DC, 1971), Academic Press, New York, pp. 55-70.
7. Halanay A. Differential equations: Stability, oscillations, time lags. 1966;Academic Press, New York-London.
8. Khalil H.K. Nonlinear systems. 1992;Macmillan Publishing Company, New York.
9. Li X.-J. On the absolute stability of systems with time lags. Chinese Mathematics. 4:1963;609-626.
10. Naumov B.N., Tsypkin Y.Z. A frequency criterion for absolute process stability in nonlinear automatic control systems. Avtomatika i Telemekhanika. 25(6):1964;852-867.
11. ∞ memoryless control with an α -stability constraint for time-delay systems An LMI approach IEEE Transactions on Automatic Control. 43(5):1998;739-743.
12. Popov V.M., Halanay A. On the stability of nonlinear automatic control systems with lagging argument. Automation Remote Control. 23:1962;783-786.
13. Rekasius Z.V., Gibson J.E. Stability analysis of nonlinear control systems by the second method of Lyapunov. IRE Transactions on Automatic Control. AC-7(1):1962;3-15.
14. Sun Y.-J., Hsieh J.-G. On. α -stability criteria of nonlinear systems with multiple time delays Journal of Franklin Institute. 335B(4):1998;695-705.
15. Wang R.-J., Wang W.-J. α -stability analysis of perturbed systems with multiple noncommensurate time delays IEEE Transactions on Circuits and Systems - I. 43(4):1996;349-352.