Characterizing families of positive real matrices by matrix substitutions on scalar rational functions

This paper concerns the characterization of positive real matrices generated by substitutions (of the Laplace variable s) in scalar rational transfer function by matrix positive real functions. Our main results are restricted to both strongly strictly positive real matrices arid strictly bounded real matrices. As a way to illustrate our main results, we also include here a partial extension of both the Kalman-Yakubovich-Popov lemma (for strongly strictly positive real systems of zero relative degree) and the circle criterion (for strictly positive real systems of zero relative degree).

[1]  Brian D. O. Anderson,et al.  Robust strict positive realness: characterization and construction , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[2]  Antonio Vicino,et al.  New results for the design of robust strict positive real systems , 1992, [Proceedings] 1992 IEEE International Symposium on Circuits and Systems.

[3]  J. Wen.  Time domain and frequency domain conditions for strict positive realness , 1988 .

[4]  D. S. Bernstein,et al.  Explicit construction of quadratic Lyapunov functions for the small gain, positivity, circle and Popov theorems and their application to robust stability , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[5]  M. Safonov,et al.  Synthesis of positive real multivariable feedback systems , 1987 .

[6]  K. Narendra,et al.  Frequency Domain Criteria for Absolute Stability , 1973 .

[7]  V. Kharitonov.  Asympotic stability of an equilibrium position of a family of systems of linear differntial equations , 1978 .

[8]  Jacquelien M. A. Scherpen,et al.  Power shaping: a new paradigm for stabilization of nonlinear RLC circuits , 2003, IEEE Trans. Autom. Control..

[9]  Juan Carlos Martínez-García,et al.  H @ -Robustness properties preservation in SISO systems when applying SPR substitutions , 2003 .

[10]  Guillermo Fernández-Anaya,et al.  Preservation of SPR functions and stabilization by substitutions in SISO plants , 1999, IEEE Trans. Autom. Control..

[11]  Walterio W. Mayol-Cuevas,et al.  Simultaneous stabilization using evolutionary strategies , 1997 .

[12]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[13]  Johan A. K. Suykens,et al.  Identification of positive real models in subspace identification by using regularization , 2003, IEEE Trans. Autom. Control..

[14]  B. Brogliato,et al.  Dissipative Systems Analysis and Control , 2000 .

[15]  G. Fernandez-Anaya,et al.  Preservation of solvability conditions in Riccati equations when applying SPR0 substitutions , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[16]  D. Bernstein,et al.  Explicit construction of quadratic lyapunov functions for the small gain, positivity, circle, and popov theorems and their application to robust stability. part II: Discrete-time theory , 1993 .

[17]  Long Wang.  Robust stability of polynomial families under nonlinearly correlated perturbations: Boundary results with applications , 1997, 1997 European Control Conference (ECC).

[18]  Ya. Z. Tsypkin,et al.  STABILITY AND ROBUST STABILITY OF UNIFORM SYSTEMS , 1996 .

[19]  Jose C. Geromel,et al.  Synthesis of Positive Real 7iz Controllers , 1996 .

[20]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[21]  P. Lancaster,et al.  The theory of matrices : with applications , 1985 .

[22]  B. Noble.  Applied Linear Algebra , 1969 .

[23]  Louis Weinberg,et al.  Network Analysis and Synthesis , 1962 .

[24]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[25]  José Claudio Geromel,et al.  Synthesis of positive real H2 controllers , 1997, IEEE Trans. Autom. Control..

[26]  J. W. Modestino,et al.  Adaptive Control , 1998 .

[27]  Brian D. O. Anderson,et al.  Stability of adaptive systems: passivity and averaging analysis , 1986 .

[28]  Jose C. Geromel,et al.  Synthesis of positive real /spl Hscr//sub 2/ controllers , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[29]  Guillermo Fernández-Anaya,et al.  MIMO systems properties preservation under SPR substitutions , 2004, IEEE Transactions on Circuits and Systems II: Express Briefs.

[30]  Anuradha M. Annaswamy,et al.  Stable Adaptive Systems , 1989 .