Robust stability under mixed time-varying, time-invariant and parametric uncertainty

Robustness analysis is considered for systems with structured uncertainty involving a combination of linear time-invariant and linear time-varying perturbations, and parametric uncertainty. A necessary and sufficient condition for robust stability in terms of the structured singular value μ is obtained, based on a finite augmentation of the original problem. The augmentation corresponds to considering the system at a fixed number of frequencies. Sufficient conditions based on scaled small-gain are also considered and characterized.

[1]  M. Athans,et al.  A multiloop generalization of the circle criterion for stability margin analysis , 1981 .

[2]  Andrew Packard,et al.  The complex structured singular value , 1993, Autom..

[3]  Geir E. Dullerud.  Control of Uncertain Sampled-Data Systems , 1995 .

[4]  F. Paganini.  Sets and Constraints in the Analysis Of Uncertain Systems , 1996 .

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

[6]  K. Poolla,et al.  Robust performance against time-varying structured perturbations , 1995, IEEE Trans. Autom. Control..

[7]  Peter M. Young,et al.  Robustness with parametric and dynamic uncertainty , 1993 .

[8]  Hari Bercovici,et al.  Structured Interpolation Theory , 1990 .

[9]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[10]  J. Shamma.  Robust stability with time-varying structured uncertainty , 1994, IEEE Trans. Autom. Control..

[11]  M. Khammash,et al.  Performance robustness of discrete-time systems with structured uncertainty , 1991 .

[12]  Anders Rantzer.  Uncertainties With Bounded Rates of Variation , 1993 .

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

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

[15]  Fernando Paganini,et al.  Analysis of implicitly defined systems , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[16]  丸山 徹.  Convex Analysisの二,三の進展について , 1977 .

[17]  A. Tits,et al.  Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics , 1991 .

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

[19]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[20]  Fernando Paganini,et al.  Analysis of systems with combined time invariant/time varying structured uncertainty , 1995, Proceedings of 1995 American Control Conference - ACC'95.

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