Robustness Margin Calculation with Dynamic and Real Parametric Uncertainty

The problem of Robust stability in feedback control systems with real uncertain parameters and unmodeled dynamics where the latter takes the form of one complex block dynamic uncertainty is considered. A robustness margin rm is defined with respect to such model uncertainty structure and robust stability is characterized in terms of it. An algorithm to calculate rm and the closely related Multivariable Stability Margin km and Structured Singular Value ¿ measures of Robust Stability is developed. It is shown that other control problems such as robust performance for real parametric uncertainty can also be handled in this framework.

[1]  A. Cohn,et al.  Über die Anzahl der Wurzeln einer algebraischen Gleichung in einem Kreise , 1922 .

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

[3]  A. Laub,et al.  Feedback properties of multivariable systems: The role and use of the return difference matrix , 1981 .

[4]  M. Safonov.  Stability margins of diagonally perturbed multivariable feedback systems , 1981, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[5]  G. Stein,et al.  Multivariable feedback design: Concepts for a classical/modern synthesis , 1981 .

[6]  Gene F. Franklin,et al.  Feedback Control of Dynamic Systems , 1986 .

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

[8]  A. Tits,et al.  Characterization and efficient computation of the structured singular value , 1986 .

[9]  Douglas Looze,et al.  Unmodeled dynamics: Performance and stability via parameter space methods , 1987, 26th IEEE Conference on Decision and Control.

[10]  Huang Lin,et al.  Root locations of an entire polytope of polynomials: It suffices to check the edges , 1987, 1987 American Control Conference.

[11]  K. Wei,et al.  Robust stabilizability for linear systems with both parameter variation and unstructured uncertainty , 1987, 26th IEEE Conference on Decision and Control.

[12]  B. Barmish.  Kharitonov's theorem and its extensions and applications: An introduction , 1987, 26th IEEE Conference on Decision and Control.

[13]  J. Doyle,et al.  Uncertain Multivariable Systems from a State Space Perspective , 1987, 1987 American Control Conference.

[14]  Pramod P. Khargonekar,et al.  Robust stability of feedback control systems with uncertain parameters and unmodeled dynamics , 1988, 1988 American Control Conference.

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

[16]  A. Sideris,et al.  Robustness with real parametric and structured complex uncertainty , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

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

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