Stability of polytopic systems via convex \(M\)-matrices and parameter-dependent Lyapunov functions
The authors are interested in the set \({\mathbf M}_n\) of \(M\)-matrices. They are matrices whose off diagonal elements are nonpositive, and whose eigenvalues have positive real parts. It is well known that in general the sum or a convex combination of \(M\)-matrices is not an \(M\)-matrix. The main objective of the paper is to derive a number of sufficient conditions which can be used to check that all the matrices of a polytope are \(M\)-matrices, by testing only the vertices. The results are applied to the stability problem of uncertain linear and nonlinear systems.
scientific article; zbMATH DE number 1472239
scientific article