IEEE Transactions on Automatic Control, Vol.61, No.3, 748-753, 2016
On the Analysis of the Eigenvalues of Uncertain Matrices by mu and nu: Applications to Bifurcation Avoidance and Convergence Rates
Based on the structured singular value mu and the skewed structured singular value nu, this technical note presents several useful relationships between an uncertain matrix expressed in a linear fractional form and its eigenvalues. The results are used to derive 1) sufficient conditions to avoid bifurcations for systems with parametric uncertainties and 2) bounds on the convergence rate for uncertain stable matrices and uncertain Markov matrices. Illustrative examples are also provided.