A note on spectral conditions for positive realness of single-input-single-output systems with strictly proper transfer functions

IEEE Transactions on Automatic Control

Volumn 51, Issue 5, 2006, Pages 897-900

  Zeheb, Ezra ^a,b   Shorten, Robert ^c  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^b JERUSALEM COLLEGE OF ENGINEERING   (Israel)

^c NATIONAL UNIVERSITY OF IRELAND   (Ireland)

Author keywords

Circle criterion; Eigenvalues locations; Positive real (PR) conditions; State space representation; Time varying systems

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; MATRIX ALGEBRA; NUMERICAL METHODS; SPECTRUM ANALYSIS; STATE ESTIMATION; STATE SPACE METHODS; TIME VARYING CONTROL SYSTEMS; TRANSFER FUNCTIONS;

CIRCLE CRITERION; POSITIVE REAL CONDITIONS; SINGLE-INPUT-SINGLE-OUTPUT SYSTEMS;

CONTROL SYSTEM ANALYSIS;

EID: 33646909372     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2006.872829     Document Type: Article

References (9)

1. K. Narendra and A. Annaswamy, Stable Adaptive Systems. Upper Saddle River, NJ: Prentice-Hall, 1989.
2. K. Narendra and J. Taylor, Frequency Domain Criteria for Absolute Stability. New York: Academic, 1973.
3. M. Vidysagar, Nonlinear Systems Analysis. Upper Saddle River, NJ: Prentice-Hall, 1993.
4. Z. Bai and W. Freund, "Eigenvalue based characterization and test for positive realness of scalar transfer functions," IEEE Trans. Autom. Control, vol. 45, no. 12, pp. 2396-2402, Dec. 2000.
5. W. Gao and Y. Zhou, "Eigenvalue based algorithms for testing positive realness of SISO systems," IEEE Trans. Autom. Control, vol. 48, no. 11, pp. 2051-2054, Nov. 2003.
6. J. Wen, "Time domain and frequency domain conditions for strict positive realness," IEEE Trans. Autom. Control, vol. 33, no. 10, pp. 988-992, Oct. 1988.
7. R. Shorten and K. S. Narendra, "Spectral conditions for positive realness of SISO systems," IEEE Trans. Autom. Control, vol. 49, no. 10, pp. 1875-1877, Oct. 2004.
8. G. Temes and J. LaPatra, Introduction to Circuit Synthesis and Design. New York: McGraw-Hill, 1977.
9. R. Shorten and K. S. Narendra, "On common quadratic Lyapunov functions for pairs of stable LTI systems whose system matrices are in companion form," IEEE Trans. Autom. Control, vol. 48, no. 4, pp. 618-621, Apr. 2003.