A topological result on strong stabilization problem

This note studies the robustness of nonstrong stabilizability. We consider single-input-single-output (SISO) continuous time linear systems under graph topology. A key contribution of this note is to show that there are two classes of nonstrongly stabilizable systems: One which contains plants that can be rendered strongly stabilizable by an arbitrary small perturbation, and the other which contains plants that are inherently nonstrongly stabilizable, even if perturbed. An easily implemented test referred to as weak parity interlacing property, is developed to check in which class a given model lies.

[1]  D. Youla,et al.  Single-loop feedback-stabilization of linear multivariable dynamical plants , 1974, Autom..

[2]  S. Wang,et al.  Simultaneous robust stabilisation of two normalised coprime factor plant balls , 1994 .

[3]  A. Nazli Gündes,et al.  Simultaneous stabilization of linear systems under stable additive or feedback perturbations , 1995, IEEE Trans. Autom. Control..

[4]  J. Murray,et al.  Fractional representation, algebraic geometry, and the simultaneous stabilization problem , 1982 .

[5]  A. N. Gundes,et al.  Simultaneous stabilization of systems with zeros at infinity or zero , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[6]  Andrey V. Savkin.  Simultaneous H ∞ control of a finite collection of linear plants with a single nonlinear digital controller , 1998 .

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

[8]  K. Glover,et al.  Robust stabilization of normalized coprime factor plant descriptions with H/sub infinity /-bounded uncertainty , 1989 .

[9]  James Lam,et al.  Brief On simultaneous H∞ control and strong H∞ stabilization , 2000 .

[10]  M. Zeren,et al.  On the strong stabilization problem and performance of stable /spl Hscr//sup /spl infin// controllers , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[11]  Mathukumalli Vidyasagar,et al.  Robust controllers for uncertain linear multivariable systems , 1984, Autom..

[12]  A. Nazli Gündes,et al.  Simultaneously stabilizing controller design for a class of MIMO systems , 2001, Autom..

[13]  M. Vidyasagar,et al.  Algebraic design techniques for reliable stabilization , 1982 .

[14]  Malcolm C. Smith,et al.  On the order of stable compensators , 1986, Autom..

[15]  J. Pearson.  Linear multivariable control, a geometric approach , 1977 .

[16]  Myung-Gon Yoon.  Minimizing a convex combination of the overshoot and undershoot , 2001, Syst. Control. Lett..