Robust stability under structured and unstructured perturbations Academic Article uri icon


  • In this paper, we deal with the problem of robust stability for linear time-invariant single-input single-output control systems subject to both structured (parametric) and unstructured (H) perturbations. We first present a generalization of the small gain theorem which yields necessary and sufficient conditions for robust stability of a linear time-invariant dynamic system under perturbations of mixed type. The solution involves calculating the H-norm of a finite number (at most 16) of extremal plants. The problem of calculating the exact structured and unstructured stability margins is then constructively solved. We next consider a feedback control system containing a linear time-invariant plant which is subject to both structured and unstructured perturbations. The case where the system to be controlled is interval (i.e., the transfer function coefficients vary in prescribed intervals) is treated, and a nonconservative easily verifiable necessary and sufficient condition for robust stability is given. The solution is based on the extremal property of a finite number (at most 32) of line segments in the plant parameter space along which the points closest to instability are encountered. These extremal segments were first introduced in [1] where they played a key role in the generalization of Kharitonov's theorem. In the present paper, they shed light on the geometry of the stability domain when perturbations of mixed type are present. 1990 IEEE

published proceedings

  • IEEE Transactions on Automatic Control

author list (cited authors)

  • Chapellat, H., Dahleh, M. A., & Bhattacharyya, S. P.

citation count

  • 109

complete list of authors

  • Chapellat, H||Dahleh, MA||Bhattacharyya, SP

publication date

  • January 1990