On the estimation of the real stability radius 1

Abstract Computationally efficient estimates for the real stability radius of a system matrix are developed for continuous and discrete time systems. The Frobenius norm is used instead of the operator norm and the estimates involve only the stability reserve of the system matrix and the eigenvalues of the Gram matrix of real and imaginary parts of the eigenvectors of the system matrix. A version of the estimate for a class of infinite dimensional systems is presented.