A Branch and Bound Method to Check the Stability of a Polytope of Matrices
Hideki Kokame, Takehiro Mori · Birkhäuser Basel eBooks · 1992
The stability of a linear time-invariant system which has uncertain parameters is often reduced to the stability of a polytope of matrices. To determine whether the matrix polytope is stable or not, the present paper proposes a branch and bound method which is based on the polytopic Lyapunov functions approach. The stability criterion involved is obtained from evaluating a lower bound of degree of stability. A matrix which attains the lower bound might be anticipated to give the worst degree of stability. Thus we check the instability of such an element matrix. Some examples are shown to illustrate the performance of our method. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.