Branch and Bound Algorithm for Computing the Minimum Stability Degree of Parameter-Dependent Linear Systems

V. Balakrishnan, S. Boyd, and S. Balemi

International Journal of Robust and Nonlinear Control, 1(4):295-317, October-December 1992.
Conference version, with title Computation of the minimum stability degree of parameter-dependent linear systems by a branch and bound algorithm, appeared in Proceedings of 1st IFAC Symposium on Design Methods of Control Systems, V. Balakrishnan, S. Balemi, and S Boyd, Zurich, Switzerland, pp.133-138, September 1991.

We consider linear systems with unspecified parameters that lie between given upper and lower bounds. Except for a few special cases, the computation of many quantities of interest for such systems can be performed only through an exhaustive search in parameter space. We present a general branch and bound algorithm that implements this search in a systematic manner and apply it to computing the minimum stability degree.