Fast parallel-frequency-sweeping algorithms for robust D-stability margin

This paper considers the robust D-stability margin problem under polynomic structured real parametric uncertainty. Based on the work of de Gaston and Safonov (1988), we have developed techniques such as, a parallel-frequency-sweeping strategy, different domain-splitting schemes, which significantly reduce the computational complexity and guarantee the convergence.

[1]  Athanasios Sideris,et al.  Multivariable stability margin calculation with uncertain correlated parameters , 1986, 1986 25th IEEE Conference on Decision and Control.

[2]  M. Safonov,et al.  Exact calculation of the multiloop stability margin , 1988 .

[3]  Peter M. Young,et al.  Mixed μ problems and branch and bound techniques , 1997 .

[4]  K. Sondergeld A generalization of the Routh-Hurwitz stability criteria and an application to a problem in robust controller design , 1983 .

[5]  M. Milanese,et al.  Computation of nonconservative stability perturbation bounds for systems with nonlinearly correlated uncertainties , 1990 .

[6]  John C. Doyle Analysis of Feedback Systems with Structured Uncertainty , 1982 .

[7]  C. Desoer,et al.  Linear System Theory , 1963 .

[8]  B. Ross Barmish,et al.  New Tools for Robustness of Linear Systems , 1993 .

[9]  M. Morari,et al.  Computational complexity of μ calculation , 1994, IEEE Trans. Autom. Control..

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

[11]  W. J. Duncan,et al.  On the Criteria for the Stability of Small Motions , 1929 .

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

[13]  P.M. Young,et al.  Mixed mu problems and branch and bound techniques , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[14]  Chi-Tsong Chen,et al.  Linear System Theory and Design , 1995 .

[15]  Robust analysis of feedback systems with parametric and dynamic structured uncertainty , 1989 .

[16]  Balas,et al.  [ z-analysis and Synthesis Toolbox * ( p-tools ) t , 2002 .

[17]  Svatopluk Poljak,et al.  Checking robust nonsingularity is NP-hard , 1993, Math. Control. Signals Syst..

[18]  Pramod P. Khargonekar,et al.  Robustness margin need not be a continuous function of the problem data , 1990 .

[19]  Ricardo S. Sanchez Pena,et al.  A General Program to Compute the Multivariable Stability Margin for Systems with Parametric Uncertainty , 1988, 1988 American Control Conference.

[20]  Richard D. Braatz,et al.  Computational Complexity of , 2007 .

[21]  Wai-Chuen Gan Robust and optimal control of AC machines , 2001 .

[22]  Athanasios Sideris,et al.  Fast Computation of the Multivariable Stability Margin for Real Interrelated Uncertain Parameters , 1988, 1988 American Control Conference.

[23]  Athanasios Sideris Robustness Analysis with Real Parametric Uncertainty , 2018, The Control Systems Handbook.

[24]  Calculation of the Multiloop Stability Margin , 1986, 1986 American Control Conference.