The graph metric for unstable plants and robustness estimates for feedback stability

In this paper, a "graph metric" is defined that provides a measure of the distance between unstable multivariable plants. The graph metric induces a "graph topology" on unstable plants, which is the weakest possible topology in which feedback stability is robust. Using the graph metric, it is possible to derive estimates for the robustness of feedback stability without assuming that the perturbed and unperturbed plants have the same number of RHP poles. If the perturbed and unperturbed systems have the same RHP poles, then it is possible to obtain necessary and sufficient conditions for robustness with respect to a given class of perturbations. As an application of these results, the design of stabilizing controllers for unstable singularly perturbed systems is studied.

[1]  Hassan K. Khalil,et al.  ON THE ROBUSTNESS OF OUTPUT FEEDBACK CONTROL METHODS TO MODELING ERRORS. , 1981 .

[2]  D. Youla,et al.  On the factorization of rational matrices , 1961, IRE Trans. Inf. Theory.

[3]  J. H. Wilkinson.  The algebraic eigenvalue problem , 1966 .

[4]  C. Foias,et al.  Harmonic Analysis of Operators on Hilbert Space , 1970 .

[5]  Jose B. Cruz,et al.  Feedback systems , 1971 .

[6]  W. Wolovich.  Linear multivariable systems , 1974 .

[7]  Charles A. Desoer,et al.  Open-loop unstable convolution feedback systems with dynamical feedbacks , 1976, Autom..

[8]  P. Kokotovic,et al.  Eigenvalue Placement in Two-Time-Scale Systems , 1976 .

[9]  M. Vidyasagar.  On the use of right-coprime factorizations in distributed feedback systems containing unstable subsystems , 1978 .

[10]  C. Desoer,et al.  Feedback system design: The fractional representation approach to analysis and synthesis , 1979, 1979 18th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[11]  Thomas Kailath,et al.  Linear Systems , 1980 .

[12]  M. Vidyasagar,et al.  Algebraic and topological aspects of feedback stabilization , 1980 .

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

[14]  J. Murray,et al.  Feedback system design: The tracking and disturbance rejection problems , 1981 .

[15]  Bruce A. Francis,et al.  Algebraic and topological aspects of the regulator problem for lumped linear systems , 1983, Autom..