Matrix pencil and matrix measure methods for robust stability in real parameter spaces

The authors report on a study of robust stability in a real parameter space for robot polynomial type spaces and matrix type spaces. Using the Sylvester resultant matrix or the Kronecker sum the robust stability question can be converted into a generalized eigenvalue problem of a matrix pencil. Some sufficient and necessary conditions are given. The admissible perturbation set is also defined. This set can be found via a generalized eigenvalue computation. A method is proposed to compute a polytope to approximate a maximal admissible perturbation set via a matrix measure. Some results can be extended to the discrete-time case